{
  "title": "Factorisation of Polynomials - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Factorise: x² + 5x + 6", "options": {"A": "(x+2)(x+3)", "B": "(x+1)(x+6)", "C": "(x-2)(x-3)", "D": "(x+2)(x-3)"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Factorise: x² - 7x + 12", "options": {"A": "(x-3)(x-4)", "B": "(x+3)(x+4)", "C": "(x-2)(x-6)", "D": "(x+2)(x+6)"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Factorise: x² - x - 6", "options": {"A": "(x-3)(x+2)", "B": "(x+3)(x-2)", "C": "(x-1)(x+6)", "D": "(x+1)(x-6)"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Factorise: x² + 8x + 15", "options": {"A": "(x+3)(x+5)", "B": "(x+1)(x+15)", "C": "(x-3)(x-5)", "D": "(x+2)(x+7.5)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Factorise: x² - 5x + 6", "options": {"A": "(x-2)(x-3)", "B": "(x+2)(x+3)", "C": "(x-1)(x-6)", "D": "(x+1)(x+6)"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Factorise: x² - 9", "options": {"A": "(x-3)(x+3)", "B": "(x-9)(x+1)", "C": "(x-3)²", "D": "(x+3)²"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Factorise: x² - 16", "options": {"A": "(x-4)(x+4)", "B": "(x-8)(x+2)", "C": "(x-2)(x+8)", "D": "(x-4)²"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Factorise: x² - 25", "options": {"A": "(x-5)(x+5)", "B": "(x-10)(x+2.5)", "C": "(x-2.5)(x+10)", "D": "(x-5)²"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Factorise: x² - 49", "options": {"A": "(x-7)(x+7)", "B": "(x-14)(x+3.5)", "C": "(x-3.5)(x+14)", "D": "(x-7)²"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Factorise: x² - 100", "options": {"A": "(x-10)(x+10)", "B": "(x-20)(x+5)", "C": "(x-5)(x+20)", "D": "(x-10)²"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Factorise: 4x² - 9", "options": {"A": "(2x-3)(2x+3)", "B": "(4x-3)(x+3)", "C": "(2x-9)(2x+1)", "D": "(4x-1)(x+9)"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Factorise: 9x² - 16", "options": {"A": "(3x-4)(3x+4)", "B": "(9x-4)(x+4)", "C": "(3x-16)(3x+1)", "D": "(9x-1)(x+16)"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Factorise: 16x² - 25", "options": {"A": "(4x-5)(4x+5)", "B": "(16x-5)(x+5)", "C": "(4x-25)(4x+1)", "D": "(16x-1)(x+25)"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Factorise: 25x² - 36", "options": {"A": "(5x-6)(5x+6)", "B": "(25x-6)(x+6)", "C": "(5x-36)(5x+1)", "D": "(25x-1)(x+36)"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Factorise: x² + 10x + 25", "options": {"A": "(x+5)²", "B": "(x+10)(x+2.5)", "C": "(x+2.5)(x+10)", "D": "(x+25)(x+1)"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Factorise: x² - 6x + 9", "options": {"A": "(x-3)²", "B": "(x-6)(x+1.5)", "C": "(x-1.5)(x+6)", "D": "(x-9)(x+1)"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Factorise: x² + 12x + 36", "options": {"A": "(x+6)²", "B": "(x+12)(x+3)", "C": "(x+3)(x+12)", "D": "(x+36)(x+1)"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Factorise: x² - 14x + 49", "options": {"A": "(x-7)²", "B": "(x-14)(x+3.5)", "C": "(x-3.5)(x+14)", "D": "(x-49)(x+1)"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Factorise: x² + 16x + 64", "options": {"A": "(x+8)²", "B": "(x+16)(x+4)", "C": "(x+4)(x+16)", "D": "(x+64)(x+1)"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Factorise: x² - 20x + 100", "options": {"A": "(x-10)²", "B": "(x-20)(x+5)", "C": "(x-5)(x+20)", "D": "(x-100)(x+1)"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Factorise: 2x² + 7x + 3", "options": {"A": "(2x+1)(x+3)", "B": "(2x+3)(x+1)", "C": "(x+1)(2x+3)", "D": "(x+3)(2x+1)"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Factorise: 3x² + 10x + 3", "options": {"A": "(3x+1)(x+3)", "B": "(3x+3)(x+1)", "C": "(x+1)(3x+3)", "D": "(x+3)(3x+1)"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Factorise: 4x² + 12x + 9", "options": {"A": "(2x+3)²", "B": "(4x+3)(x+3)", "C": "(2x+9)(2x+1)", "D": "(4x+1)(x+9)"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Factorise: 9x² + 30x + 25", "options": {"A": "(3x+5)²", "B": "(9x+5)(x+5)", "C": "(3x+25)(3x+1)", "D": "(9x+1)(x+25)"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Factorise: 16x² + 40x + 25", "options": {"A": "(4x+5)²", "B": "(16x+5)(x+5)", "C": "(4x+25)(4x+1)", "D": "(16x+1)(x+25)"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Factorise: x² + xy + xz + yz", "options": {"A": "(x+y)(x+z)", "B": "(x+z)(x+y)", "C": "x(x+y+z)", "D": "(x+y)(y+z)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Factorise: ab + ac + b² + bc", "options": {"A": "(a+b)(b+c)", "B": "(a+c)(b+b)", "C": "b(a+b+c)", "D": "(a+b)(a+c)"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Factorise: xy + xz + wy + wz", "options": {"A": "(x+w)(y+z)", "B": "(x+z)(w+y)", "C": "(x+y)(w+z)", "D": "(y+z)(x+w)"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Factorise: a² + ab + ac + bc", "options": {"A": "(a+b)(a+c)", "B": "(a+c)(a+b)", "C": "a(a+b+c)", "D": "(a+b)(b+c)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Factorise: x² + ax + bx + ab", "options": {"A": "(x+a)(x+b)", "B": "(x+b)(x+a)", "C": "x(x+a+b)", "D": "(x+ab)(x+1)"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Factorise: x³ - 8", "options": {"A": "(x-2)(x²+2x+4)", "B": "(x+2)(x²-2x+4)", "C": "(x-4)(x²+4x+16)", "D": "(x+4)(x²-4x+16)"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Factorise: x³ + 27", "options": {"A": "(x+3)(x²-3x+9)", "B": "(x-3)(x²+3x+9)", "C": "(x+9)(x²-9x+81)", "D": "(x-9)(x²+9x+81)"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Factorise: 8x³ - 27", "options": {"A": "(2x-3)(4x²+6x+9)", "B": "(2x+3)(4x²-6x+9)", "C": "(4x-3)(2x²+6x+9)", "D": "(4x+3)(2x²-6x+9)"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Factorise: 64x³ + 125", "options": {"A": "(4x+5)(16x²-20x+25)", "B": "(4x-5)(16x²+20x+25)", "C": "(8x+5)(8x²-10x+25)", "D": "(8x-5)(8x²+10x+25)"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Factorise: 27x³ - 8", "options": {"A": "(3x-2)(9x²+6x+4)", "B": "(3x+2)(9x²-6x+4)", "C": "(9x-2)(3x²+6x+4)", "D": "(9x+2)(3x²-6x+4)"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Factorise: x⁴ - 16", "options": {"A": "(x-2)(x+2)(x²+4)", "B": "(x-4)(x+4)(x²+1)", "C": "(x²-4)(x²+4)", "D": "(x-2)²(x+2)²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Factorise: x⁴ - 81", "options": {"A": "(x-3)(x+3)(x²+9)", "B": "(x-9)(x+9)(x²+1)", "C": "(x²-9)(x²+9)", "D": "(x-3)²(x+3)²"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Factorise: 16x⁴ - 81", "options": {"A": "(2x-3)(2x+3)(4x²+9)", "B": "(4x-9)(4x+9)(x²+1)", "C": "(4x²-9)(4x²+9)", "D": "(2x-3)²(2x+3)²"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Factorise: x⁴ - y⁴", "options": {"A": "(x-y)(x+y)(x²+y²)", "B": "(x²-y²)(x²+y²)", "C": "(x-y)²(x+y)²", "D": "(x-y)(x+y)(x-y)(x+y)"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Factorise: 81x⁴ - 16y⁴", "options": {"A": "(3x-2y)(3x+2y)(9x²+4y²)", "B": "(9x²-4y²)(9x²+4y²)", "C": "(3x-2y)²(3x+2y)²", "D": "(9x-4y)(9x+4y)(x²+y²)"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Factorise: x² - y² - 2y - 1", "options": {"A": "(x-y-1)(x+y+1)", "B": "(x-y+1)(x+y-1)", "C": "(x-1)(x+1)-y(y+2)", "D": "(x-y)(x+y)-2y-1"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Factorise: x² - y² - 4y - 4", "options": {"A": "(x-y-2)(x+y+2)", "B": "(x-y+2)(x+y-2)", "C": "(x-2)(x+2)-y(y+4)", "D": "(x-y)(x+y)-4y-4"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Factorise: x² - y² - 6y - 9", "options": {"A": "(x-y-3)(x+y+3)", "B": "(x-y+3)(x+y-3)", "C": "(x-3)(x+3)-y(y+6)", "D": "(x-y)(x+y)-6y-9"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Factorise: x² - y² - 8y - 16", "options": {"A": "(x-y-4)(x+y+4)", "B": "(x-y+4)(x+y-4)", "C": "(x-4)(x+4)-y(y+8)", "D": "(x-y)(x+y)-8y-16"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Factorise: x² - y² - 10y - 25", "options": {"A": "(x-y-5)(x+y+5)", "B": "(x-y+5)(x+y-5)", "C": "(x-5)(x+5)-y(y+10)", "D": "(x-y)(x+y)-10y-25"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Factorise: 4x² - 12xy + 9y²", "options": {"A": "(2x-3y)²", "B": "(4x-3y)(x-3y)", "C": "(2x-9y)(2x-y)", "D": "(4x-y)(x-9y)"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Factorise: 9x² - 24xy + 16y²", "options": {"A": "(3x-4y)²", "B": "(9x-4y)(x-4y)", "C": "(3x-16y)(3x-y)", "D": "(9x-y)(x-16y)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Factorise: 16x² - 40xy + 25y²", "options": {"A": "(4x-5y)²", "B": "(16x-5y)(x-5y)", "C": "(4x-25y)(4x-y)", "D": "(16x-y)(x-25y)"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Factorise: 25x² - 60xy + 36y²", "options": {"A": "(5x-6y)²", "B": "(25x-6y)(x-6y)", "C": "(5x-36y)(5x-y)", "D": "(25x-y)(x-36y)"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Factorise: 36x² - 84xy + 49y²", "options": {"A": "(6x-7y)²", "B": "(36x-7y)(x-7y)", "C": "(6x-49y)(6x-y)", "D": "(36x-y)(x-49y)"}, "correct_answer": "A"},
   {"id":51,"difficulty":"medium","question":"Factorise: x³ + 3x² + 3x + 1","options":{"A":"(x+1)³","B":"(x-1)³","C":"(x+1)(x²+2x+1)","D":"(x-1)(x²+2x+1)"},"correct_answer":"A"},
{"id":52,"difficulty":"medium","question":"Factorise: x³ - 3x² + 3x - 1","options":{"A":"(x-1)³","B":"(x+1)³","C":"(x-1)(x²-2x+1)","D":"(x+1)(x²-2x+1)"},"correct_answer":"A"},
{"id":53,"difficulty":"medium","question":"Factorise: 8x³ + 12x² + 6x + 1","options":{"A":"(2x+1)³","B":"(2x-1)³","C":"(4x+1)(2x²+2x+1)","D":"(4x-1)(2x²+2x+1)"},"correct_answer":"A"},
{"id":54,"difficulty":"medium","question":"Factorise: 27x³ - 27x² + 9x - 1","options":{"A":"(3x-1)³","B":"(3x+1)³","C":"(3x-1)(9x²-6x+1)","D":"(3x+1)(9x²-6x+1)"},"correct_answer":"A"},
{"id":55,"difficulty":"medium","question":"Factorise: 64x³ + 48x² + 12x + 1","options":{"A":"(4x+1)³","B":"(4x-1)³","C":"(8x+1)(8x²+4x+1)","D":"(8x-1)(8x²+4x+1)"},"correct_answer":"A"},
{"id":56,"difficulty":"medium","question":"Factorise: x⁴ + x² + 1","options":{"A":"(x²+x+1)(x²-x+1)","B":"(x²+1)(x²+1)","C":"(x²+√x+1)(x²-√x+1)","D":"(x²+2x+1)(x²-2x+1)"},"correct_answer":"A"},
{"id":57,"difficulty":"medium","question":"Factorise: x⁴ + 4","options":{"A":"(x²+2x+2)(x²-2x+2)","B":"(x²+2)(x²+2)","C":"(x²+√2x+2)(x²-√2x+2)","D":"(x²+4x+1)(x²-4x+1)"},"correct_answer":"A"},
{"id":58,"difficulty":"medium","question":"Factorise: x⁴ + 4x² + 16","options":{"A":"(x²+2x+4)(x²-2x+4)","B":"(x²+4)(x²+4)","C":"(x²+4x+4)(x²-4x+4)","D":"(x²+8x+4)(x²-8x+4)"},"correct_answer":"A"},
{"id":59,"difficulty":"medium","question":"Factorise: x⁴ + 9x² + 81","options":{"A":"(x²+3x+9)(x²-3x+9)","B":"(x²+9)(x²+9)","C":"(x²+9x+9)(x²-9x+9)","D":"(x²+27x+9)(x²-27x+9)"},"correct_answer":"A"},
{"id":60,"difficulty":"medium","question":"Factorise: x⁴ + 16x² + 256","options":{"A":"(x²+4x+16)(x²-4x+16)","B":"(x²+16)(x²+16)","C":"(x²+16x+16)(x²-16x+16)","D":"(x²+64x+16)(x²-64x+16)"},"correct_answer":"A"},
{"id":61,"difficulty":"hard","question":"Factorise: x³ + y³ + z³ - 3xyz","options":{"A":"(x+y+z)(x²+y²+z²-xy-yz-zx)","B":"(x+y+z)(x²+y²+z²+xy+yz+zx)","C":"(x+y+z)³-3xyz","D":"(x+y)(y+z)(z+x)"},"correct_answer":"A"},
{"id":62,"difficulty":"hard","question":"Factorise: a³ + b³ + c³ when a+b+c=0","options":{"A":"3abc","B":"abc","C":"a³+b³+c³","D":"0"},"correct_answer":"A"},
{"id":63,"difficulty":"hard","question":"Factorise: x⁵ + x⁴ + x³ + x² + x + 1","options":{"A":"(x+1)(x²+x+1)(x²-x+1)","B":"(x-1)(x²+x+1)(x²-x+1)","C":"(x+1)(x⁴+x²+1)","D":"(x-1)(x⁴+x²+1)"},"correct_answer":"A"},
{"id":64,"difficulty":"hard","question":"Factorise: x⁶ - 1","options":{"A":"(x-1)(x+1)(x²+x+1)(x²-x+1)","B":"(x-1)(x+1)(x²+1)(x²+1)","C":"(x³-1)(x³+1)","D":"(x²-1)(x⁴+x²+1)"},"correct_answer":"A"},
{"id":65,"difficulty":"hard","question":"Factorise: x⁶ - y⁶","options":{"A":"(x-y)(x+y)(x²+xy+y²)(x²-xy+y²)","B":"(x²-y²)(x⁴+x²y²+y⁴)","C":"(x³-y³)(x³+y³)","D":"(x-y)³(x+y)³"},"correct_answer":"A"},
{"id":66,"difficulty":"hard","question":"Factorise: x⁸ - y⁸","options":{"A":"(x-y)(x+y)(x²+y²)(x⁴+y⁴)","B":"(x²-y²)(x²+y²)(x⁴+y⁴)","C":"(x⁴-y⁴)(x⁴+y⁴)","D":"(x-y)⁴(x+y)⁴"},"correct_answer":"A"},
{"id":67,"difficulty":"hard","question":"Factorise: x¹⁰ - 1","options":{"A":"(x-1)(x+1)(x⁴+x³+x²+x+1)(x⁴-x³+x²-x+1)","B":"(x-1)(x+1)(x⁸+x⁴+1)","C":"(x⁵-1)(x⁵+1)","D":"(x²-1)(x⁸+x⁶+x⁴+x²+1)"},"correct_answer":"A"},
{"id":68,"difficulty":"hard","question":"Factorise: x¹² - y¹²","options":{"A":"(x-y)(x+y)(x²+xy+y²)(x²-xy+y²)(x²+y²)(x⁴-x²y²+y⁴)","B":"(x⁶-y⁶)(x⁶+y⁶)","C":"(x⁴-y⁴)(x⁸+x⁴y⁴+y⁸)","D":"(x³-y³)(x³+y³)(x⁶+y⁶)"},"correct_answer":"A"},
{"id":69,"difficulty":"hard","question":"Factorise: (x²+3x+2)(x²+7x+12) - 24","options":{"A":"(x+4)(x+6)(x²+5x)","B":"(x+2)(x+3)(x²+7x)","C":"(x+1)(x+5)(x²+6x)","D":"(x+4)(x+3)(x²+6x)"},"correct_answer":"A"},
{"id":70,"difficulty":"hard","question":"Factorise: (x²+5x+4)(x²+5x+6) - 15","options":{"A":"(x²+5x+9)(x²+5x+1)","B":"(x²+5x+7)(x²+5x+3)","C":"(x²+5x+5)(x²+5x+5)","D":"(x²+5x+8)(x²+5x+2)"},"correct_answer":"A"},
{"id":71,"difficulty":"hard","question":"Factorise: (x²+8x+7)(x²+8x+15) + 15","options":{"A":"(x²+8x+10)(x²+8x+12)","B":"(x²+8x+9)(x²+8x+13)","C":"(x²+8x+8)(x²+8x+14)","D":"(x²+8x+11)(x²+8x+11)"},"correct_answer":"A"},
{"id":72,"difficulty":"hard","question":"Factorise: (x²+3x)² - 2(x²+3x) - 8","options":{"A":"(x²+3x-4)(x²+3x+2)","B":"(x²+3x-2)(x²+3x+4)","C":"(x²+3x-1)(x²+3x+8)","D":"(x²+3x-8)(x²+3x+1)"},"correct_answer":"A"},
{"id":73,"difficulty":"hard","question":"Factorise: (x²+5x)² - 4(x²+5x) - 12","options":{"A":"(x²+5x-6)(x²+5x+2)","B":"(x²+5x-2)(x²+5x+6)","C":"(x²+5x-3)(x²+5x+4)","D":"(x²+5x-4)(x²+5x+3)"},"correct_answer":"A"},
{"id":74,"difficulty":"hard","question":"Factorise: x⁴ + 2x³ + 3x² + 2x + 1","options":{"A":"(x²+x+1)²","B":"(x²-x+1)²","C":"(x²+1)(x²+2x+1)","D":"(x²+x)²+2(x²+x)+1"},"correct_answer":"A"},
{"id":75,"difficulty":"hard","question":"Factorise: x⁴ - 2x³ + 3x² - 2x + 1","options":{"A":"(x²-x+1)²","B":"(x²+x+1)²","C":"(x²-1)(x²-2x+1)","D":"(x²-x)²+2(x²-x)+1"},"correct_answer":"A"},
{"id":76,"difficulty":"hard","question":"Factorise: 4x⁴ + 1","options":{"A":"(2x²+2x+1)(2x²-2x+1)","B":"(2x²+1)(2x²+1)","C":"(2x²+√2x+1)(2x²-√2x+1)","D":"(2x²+4x+1)(2x²-4x+1)"},"correct_answer":"A"},
{"id":77,"difficulty":"hard","question":"Factorise: 9x⁴ + 4","options":{"A":"(3x²+2x+2)(3x²-2x+2)","B":"(3x²+2)(3x²+2)","C":"(3x²+√6x+2)(3x²-√6x+2)","D":"(3x²+4x+2)(3x²-4x+2)"},"correct_answer":"A"},
{"id":78,"difficulty":"hard","question":"Factorise: 16x⁴ + 81","options":{"A":"(4x²+6x+9)(4x²-6x+9)","B":"(4x²+9)(4x²+9)","C":"(4x²+12x+9)(4x²-12x+9)","D":"(4x²+18x+9)(4x²-18x+9)"},"correct_answer":"A"},
{"id":79,"difficulty":"hard","question":"Factorise: (a+b)³ + (b+c)³ + (c+a)³ - 3(a+b)(b+c)(c+a)","options":{"A":"2(a+b+c)(a²+b²+c²-ab-bc-ca)","B":"(a+b+c)(a²+b²+c²-ab-bc-ca)","C":"3(a+b+c)(a²+b²+c²-ab-bc-ca)","D":"4(a+b+c)(a²+b²+c²-ab-bc-ca)"},"correct_answer":"A"},
{"id":80,"difficulty":"hard","question":"Factorise: (x+y+z)³ - x³ - y³ - z³","options":{"A":"3(x+y)(y+z)(z+x)","B":"(x+y)(y+z)(z+x)","C":"2(x+y)(y+z)(z+x)","D":"4(x+y)(y+z)(z+x)"},"correct_answer":"A"},
{"id":81,"difficulty":"hard","question":"Factorise: a³(b-c) + b³(c-a) + c³(a-b)","options":{"A":"(a-b)(b-c)(c-a)(a+b+c)","B":"(a-b)(b-c)(c-a)(ab+bc+ca)","C":"(a-b)(b-c)(c-a)(a²+b²+c²)","D":"(a-b)(b-c)(c-a)(a²b+b²c+c²a)"},"correct_answer":"A"},
{"id":82,"difficulty":"hard","question":"Factorise: a(b²+c²) + b(c²+a²) + c(a²+b²) + 3abc","options":{"A":"(a+b+c)(ab+bc+ca)","B":"(a+b)(b+c)(c+a)","C":"a²b+b²c+c²a+abc","D":"(a+b+c)(a²+b²+c²)"},"correct_answer":"A"},
{"id":83,"difficulty":"hard","question":"Factorise: a⁴ + b⁴ + c⁴ - 2a²b² - 2b²c² - 2c²a²","options":{"A":"(a+b+c)(a+b-c)(a-b+c)(a-b-c)","B":"(a²+b²+c²)(a²+b²-c²)(a²-b²+c²)","C":"(a+b)²(a-b)²+(b+c)²(b-c)²+(c+a)²(c-a)²","D":"a⁴+b⁴+c⁴-2a²b²-2b²c²-2c²a²"},"correct_answer":"A"},
{"id":84,"difficulty":"hard","question":"Factorise: x⁸ + x⁴ + 1","options":{"A":"(x²+x+1)(x²-x+1)(x⁴-x²+1)","B":"(x⁴+x²+1)(x⁴-x²+1)","C":"(x²+1)(x⁴+x²+1)(x²-1)","D":"(x⁴+1)(x⁴+1)"},"correct_answer":"A"},
{"id":85,"difficulty":"hard","question":"Factorise: x¹⁰ + x⁵ + 1","options":{"A":"(x²+x+1)(x²-x+1)(x⁶-x³+1)","B":"(x⁵+x+1)(x⁵-x+1)","C":"(x²+1)(x⁸-x⁴+1)","D":"(x⁵+1)(x⁵+1)"},"correct_answer":"A"},
{"id":86,"difficulty":"hard","question":"Factorise: x¹⁴ + x⁷ + 1","options":{"A":"(x²+x+1)(x²-x+1)(x¹⁰-x⁵+1)","B":"(x⁷+x+1)(x⁷-x+1)","C":"(x²+1)(x¹²-x⁶+1)","D":"(x⁷+1)(x⁷+1)"},"correct_answer":"A"},
{"id":87,"difficulty":"hard","question":"Factorise: a⁶ - 7a³ - 8","options":{"A":"(a-2)(a²+2a+4)(a+1)(a²-a+1)","B":"(a³-8)(a³+1)","C":"(a²-2)(a⁴+2a²+4)(a²+1)(a⁴-a²+1)","D":"(a-2)(a+2)(a²+4)(a+1)(a²+1)"},"correct_answer":"A"},
{"id":88,"difficulty":"hard","question":"Factorise: x⁶ - 26x³ - 27","options":{"A":"(x-3)(x²+3x+9)(x+1)(x²-x+1)","B":"(x³-27)(x³+1)","C":"(x-3)(x+3)(x²+9)(x+1)(x²+1)","D":"(x²-3)(x⁴+3x²+9)(x²+1)(x⁴-x²+1)"},"correct_answer":"A"},
{"id":89,"difficulty":"hard","question":"Factorise: x⁸ - 15x⁴ - 16","options":{"A":"(x²+4)(x²-4)(x²+1)(x²-1)","B":"(x⁴-16)(x⁴+1)","C":"(x²+4)(x²-4)(x⁴+1)","D":"(x⁴-16)(x²+1)(x²-1)"},"correct_answer":"A"},
{"id":90,"difficulty":"hard","question":"Factorise: x¹⁰ - 31x⁵ - 32","options":{"A":"(x²+2x+4)(x²-2x+4)(x+1)(x²-x+1)(x²+2)(x²-2)","B":"(x⁵-32)(x⁵+1)","C":"(x²+4)(x²-4)(x⁶+1)","D":"(x⁵-32)(x²+1)(x³-1)"},"correct_answer":"A"},
{"id":91,"difficulty":"hard","question":"Factorise: (x+1)(x+2)(x+3)(x+4) - 15","options":{"A":"(x²+5x+5)(x²+5x+7)","B":"(x²+5x+3)(x²+5x+9)","C":"(x²+5x+1)(x²+5x+11)","D":"(x²+5x)(x²+5x+12)"},"correct_answer":"A"},
{"id":92,"difficulty":"hard","question":"Factorise: (x+1)(x+2)(x+3)(x+6) - 3x²","options":{"A":"(x²+6x+6)(x²+6x+6)","B":"(x²+6x+4)(x²+6x+9)","C":"(x²+6x+3)(x²+6x+12)","D":"(x²+6x+2)(x²+6x+18)"},"correct_answer":"A"},
{"id":93,"difficulty":"hard","question":"Factorise: (x+2)(x+3)(x+4)(x+5) - 24","options":{"A":"(x²+7x+6)(x²+7x+10)","B":"(x²+7x+4)(x²+7x+12)","C":"(x²+7x+2)(x²+7x+14)","D":"(x²+7x)(x²+7x+16)"},"correct_answer":"A"},
{"id":94,"difficulty":"hard","question":"Factorise: (x+1)(x+2)(x+4)(x+5) - 9","options":{"A":"(x²+6x+7)(x²+6x+7)","B":"(x²+6x+5)(x²+6x+9)","C":"(x²+6x+3)(x²+6x+11)","D":"(x²+6x+1)(x²+6x+13)"},"correct_answer":"A"},
{"id":95,"difficulty":"hard","question":"Factorise: (x+1)(x+3)(x+5)(x+7) + 15","options":{"A":"(x²+8x+5)(x²+8x+21)","B":"(x²+8x+3)(x²+8x+25)","C":"(x²+8x+7)(x²+8x+15)","D":"(x²+8x+1)(x²+8x+31)"},"correct_answer":"A"},
{"id":96,"difficulty":"hard","question":"Factorise: x⁴ + y⁴ + z⁴ - 2x²y² - 2y²z² - 2z²x²","options":{"A":"(x+y+z)(x+y-z)(x-y+z)(x-y-z)","B":"(x²+y²+z²)(x²+y²-z²)(x²-y²+z²)","C":"(x+y)²(x-y)²+(y+z)²(y-z)²+(z+x)²(z-x)²","D":"x⁴+y⁴+z⁴-2x²y²-2y²z²-2z²x²"},"correct_answer":"A"},
{"id":97,"difficulty":"hard","question":"Factorise: a⁴ + 4b⁴","options":{"A":"(a²+2ab+2b²)(a²-2ab+2b²)","B":"(a²+2b²)(a²+2b²)","C":"(a²+√2ab+2b²)(a²-√2ab+2b²)","D":"(a²+4b²)(a²+1)"},"correct_answer":"A"},
{"id":98,"difficulty":"hard","question":"Factorise: x⁴ + 64","options":{"A":"(x²+4x+8)(x²-4x+8)","B":"(x²+8)(x²+8)","C":"(x²+√8x+8)(x²-√8x+8)","D":"(x²+16x+8)(x²-16x+8)"},"correct_answer":"A"},
{"id":99,"difficulty":"hard","question":"Factorise: 81x⁴ + 4","options":{"A":"(9x²+6x+2)(9x²-6x+2)","B":"(9x²+2)(9x²+2)","C":"(9x²+√6x+2)(9x²-√6x+2)","D":"(9x²+12x+2)(9x²-12x+2)"},"correct_answer":"A"},
{"id":100,"difficulty":"hard","question":"Factorise: 16x⁴ + 81y⁴","options":{"A":"(4x²+6xy+9y²)(4x²-6xy+9y²)","B":"(4x²+9y²)(4x²+9y²)","C":"(4x²+√6xy+9y²)(4x²-√6xy+9y²)","D":"(4x²+12xy+9y²)(4x²-12xy+9y²)"},"correct_answer":"A"}
  ]}