{
  "title": "Factorization - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Factorize: 3x + 6 🧩",
      "options": {
        "A": "3(x+2)",
        "B": "3(x+6)",
        "C": "x(3+6)",
        "D": "3x(1+2)"
      },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Factor: 5y - 10 ✨",
      "options": {
        "A": "5(y-2)",
        "B": "5(y-10)",
        "C": "y(5-10)",
        "D": "5y(1-2)"
      },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "Factorize: 2a² + 4a 🔍",
      "options": {
        "A": "2a(a+2)",
        "B": "a(a+4)",
        "C": "2(a+2)",
        "D": "4a(a+1)"
      },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Factor: 7p - 14p² 🎯",
      "options": {
        "A": "7p(1-2p)",
        "B": "7(p-2p²)",
        "C": "p(7-14p)",
        "D": "7p(1+2p)"
      },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "Factorize: 12 + 8m ➕",
      "options": {
        "A": "4(3+2m)",
        "B": "2(3+4m)",
        "C": "8(1+m)",
        "D": "12(1+m)"
      },
      "correct_answer": "A"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Factor: x² - 9 🏷️",
      "options": {
        "A": "(x-3)(x+3)",
        "B": "(x-9)(x+1)",
        "C": "(x-3)²",
        "D": "x(x-9)"
      },
      "correct_answer": "A"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "Factorize: 4b² - 25 📐",
      "options": {
        "A": "(2b-5)(2b+5)",
        "B": "(4b-5)(4b+5)",
        "C": "2(b-5)(b+5)",
        "D": "(2b-25)(2b+1)"
      },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Factor: y² - 16 🧠",
      "options": {
        "A": "(y-4)(y+4)",
        "B": "(y-8)(y+2)",
        "C": "(y-16)(y+1)",
        "D": "y(y-16)"
      },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Factorize: 9k² - 1 🪀",
      "options": {
        "A": "(3k-1)(3k+1)",
        "B": "(9k-1)(9k+1)",
        "C": "3(k-1)(k+1)",
        "D": "(3k-1)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Factor: 1 - 25z² ❄️",
      "options": {
        "A": "(1-5z)(1+5z)",
        "B": "(1-25z)(1+z)",
        "C": "(5z-1)(5z+1)",
        "D": "1(1-25z)"
      },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Factorize: ax + ay 🍰",
      "options": {
        "A": "a(x+y)",
        "B": "x(a+y)",
        "C": "a(x)+a(y)",
        "D": "xy(a)"
      },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Factor: 6pq - 9q 🧮",
      "options": {
        "A": "3q(2p-3)",
        "B": "q(3p-3)",
        "C": "3(pq-q)",
        "D": "9q(p-1)"
      },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Factorize: x² + 5x + 6 📏",
      "options": {
        "A": "(x+2)(x+3)",
        "B": "(x+1)(x+6)",
        "C": "(x+5)(x+1)",
        "D": "x(x+5+6)"
      },
      "correct_answer": "A"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "Factor: m² + 7m + 12 ➖",
      "options": {
        "A": "(m+3)(m+4)",
        "B": "(m+2)(m+6)",
        "C": "(m+1)(m+12)",
        "D": "m(m+7)+12"
      },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Factorize: p² - 5p + 6 🧲",
      "options": {
        "A": "(p-2)(p-3)",
        "B": "(p-1)(p-6)",
        "C": "(p-5)(p-1)",
        "D": "p(p-5)+6"
      },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Factor: t² - t - 6 ⚖️",
      "options": {
        "A": "(t-3)(t+2)",
        "B": "(t-6)(t+1)",
        "C": "(t-2)(t+3)",
        "D": "t(t-1)-6"
      },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "Factorize: 2x² + 4x + 2 ✂️",
      "options": {
        "A": "2(x+1)²",
        "B": "2x(x+2)",
        "C": "(x+1)(x+2)",
        "D": "2x²+2"
      },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Factor: a² - b² (standard identity) 🔄",
      "options": {
        "A": "(a-b)(a+b)",
        "B": "(a-b)²",
        "C": "a(a-b)+b",
        "D": "(a+b)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "Factorize: (x+1)² - 4 🎪",
      "options": {
        "A": "(x-1)(x+3)",
        "B": "(x+1)(x-3)",
        "C": "(x+1)²-4",
        "D": "(x-2)(x+2)"
      },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Factor: 5 + 5n + 5n² ✅",
      "options": {
        "A": "5(1+n+n²)",
        "B": "5n(1+n+n²)",
        "C": "5(1+n)²",
        "D": "5(1+n)(1+n)"
      },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Factorize: 4x² - 12x + 9 🚀",
      "options": {
        "A": "(2x-3)²",
        "B": "(2x+3)²",
        "C": "(x-3)(x-3)",
        "D": "4(x-3)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "Factor: 9a² - 30ab + 25b² 🔥",
      "options": {
        "A": "(3a-5b)²",
        "B": "(3a+5b)²",
        "C": "(3a-5b)(3a+5b)",
        "D": "9(a-5b)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Factorize: 8m³ + 27n³ (sum of cubes) 🧩",
      "options": {
        "A": "(2m+3n)(4m²-6mn+9n²)",
        "B": "(2m-3n)(4m²+6mn+9n²)",
        "C": "(2m+3n)³",
        "D": "8(m+n)³"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Factor: x³ - 64y³ (difference of cubes) ⚡",
      "options": {
        "A": "(x-4y)(x²+4xy+16y²)",
        "B": "(x+4y)(x²-4xy+16y²)",
        "C": "(x-4y)³",
        "D": "x³(1-64y³)"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Factorize: x⁴ - 16 🌪️",
      "options": {
        "A": "(x-2)(x+2)(x²+4)",
        "B": "(x-4)(x+4)",
        "C": "(x²+4)²",
        "D": "x²(x²-16)"
      },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Factor: 12x² + 7x - 10 🏗️",
      "options": {
        "A": "(4x+5)(3x-2)",
        "B": "(4x-5)(3x+2)",
        "C": "(6x+5)(2x-2)",
        "D": "12(x+5)(x-2)"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Factorize: 2p² + 11p + 12 📦",
      "options": {
        "A": "(2p+3)(p+4)",
        "B": "(2p+4)(p+3)",
        "C": "(p+6)(2p+2)",
        "D": "2(p²+5.5p+6)"
      },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Factor: 15q² - 26q + 8 🎲",
      "options": {
        "A": "(5q-2)(3q-4)",
        "B": "(5q-4)(3q-2)",
        "C": "(15q-8)(q-1)",
        "D": "(5q+2)(3q+4)"
      },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Factorize: a² + 2ab + b² - c² 🌟",
      "options": {
        "A": "(a+b-c)(a+b+c)",
        "B": "(a-b-c)(a-b+c)",
        "C": "(a²+b²)-c²",
        "D": "(a+c)(b+c)"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Factor: 4 - 25(x-y)² 🚧",
      "options": {
        "A": "[2-5(x-y)][2+5(x-y)]",
        "B": "[5(x-y)-2][5(x-y)+2]",
        "C": "4-25x²+25y²",
        "D": "(x-y)(4-25)"
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Factorize: x² + 9x + 20 📈",
      "options": {
        "A": "(x+4)(x+5)",
        "B": "(x+2)(x+10)",
        "C": "(x+1)(x+20)",
        "D": "x(x+9)+20"
      },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Factor: 6y² - 5y - 6 ➗",
      "options": {
        "A": "(3y+2)(2y-3)",
        "B": "(3y-2)(2y+3)",
        "C": "(6y+1)(y-6)",
        "D": "6(y-1)(y+1)"
      },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Factorize: 9 - (m+n)² 🧠",
      "options": {
        "A": "(3-m-n)(3+m+n)",
        "B": "(9-m-n)(9+m+n)",
        "C": "(3-m+n)(3+m-n)",
        "D": "9(1-(m+n)²)"
      },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "Factor: 2a⁴ - 32b⁴ 🚅",
      "options": {
        "A": "2(a-2b)(a+2b)(a²+4b²)",
        "B": "2(a²+4b²)²",
        "C": "2(a²-16b²)",
        "D": "2(a⁴-16b⁴)"
      },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Factorize: x²y² - 4z² 🪀",
      "options": {
        "A": "(xy-2z)(xy+2z)",
        "B": "(x²y-2z)(x²y+2z)",
        "C": "y²(x²-4z²)",
        "D": "(xy-4z)(xy+z)"
      },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Factor: 27p³ - 1/8 🔑",
      "options": {
        "A": "(3p-1/2)(9p²+3p/2+1/4)",
        "B": "(3p+1/2)(9p²-3p/2+1/4)",
        "C": "27(p³-1/216)",
        "D": "(3p-1/2)³"
      },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Factorize: 5x² - 20y² ✨",
      "options": {
        "A": "5(x-2y)(x+2y)",
        "B": "(x-2y)(x+2y)",
        "C": "(5x-20y)(x+y)",
        "D": "5(x-y)(x+y)"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "Factor: (a+b)² - (a-b)² ⚖️",
      "options": {
        "A": "4ab",
        "B": "a²-b²",
        "C": "2ab",
        "D": "(a+b)(a-b)"
      },
      "correct_answer": "A"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Factorize: m⁴ + m² + 1 🎯",
      "options": {
        "A": "(m²+m+1)(m²-m+1)",
        "B": "(m²+1)²-m²",
        "C": "(m⁴+2m²+1)-m²",
        "D": "(m+1)(m³-m²+1)"
      },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Factor: 16x² + 24xy + 9y² ✅",
      "options": {
        "A": "(4x+3y)²",
        "B": "(4x-3y)²",
        "C": "(8x+3y)(2x+3y)",
        "D": "16(x+1.5y)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Factorize: x⁶ - y⁶ (as difference of squares & cubes) 🏆",
      "options": {
        "A": "(x-y)(x+y)(x²+xy+y²)(x²-xy+y²)",
        "B": "(x³-y³)(x²+y²)",
        "C": "(x-y)²(x+y)²",
        "D": "(x²-y²)(x⁴+y⁴)"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "Factor: a⁴ + 4b⁴ (by adding and subtracting 4a²b²) 🔥",
      "options": {
        "A": "(a²+2ab+2b²)(a²-2ab+2b²)",
        "B": "(a²+2b²)²",
        "C": "(a²-2b²)²",
        "D": "(a+b)⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Factorize: x³ - 3x²y + 3xy² - y³ 🧩",
      "options": {
        "A": "(x-y)³",
        "B": "(x-y)(x²+y²)",
        "C": "(x+y)³",
        "D": "(x-y)(x²-xy+y²)"
      },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Factor: 8x³ + 12x² + 6x + 1 📚",
      "options": {
        "A": "(2x+1)³",
        "B": "(2x+1)(2x²+1)",
        "C": "8(x+1)³",
        "D": "(4x+1)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Factorize: a² + b² - c² - d² + 2ab - 2cd 🌌",
      "options": {
        "A": "(a+b-c-d)(a+b+c+d)",
        "B": "(a+b)²+(c+d)²",
        "C": "(a-b)(c-d)",
        "D": "(a+c)(b+d)"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "Factor: x⁸ - y⁸ (step by step) 🐉",
      "options": {
        "A": "(x-y)(x+y)(x²+y²)(x⁴+y⁴)",
        "B": "(x²-y²)(x⁶+y⁶)",
        "C": "(x⁴-y⁴)(x²+y²)",
        "D": "(x-y)⁸"
      },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Factorize: 2x² + √5x - 5 🎲",
      "options": {
        "A": "(2x-√5)(x+√5)",
        "B": "(2x+√5)(x-√5)",
        "C": "(√5x-5)(x+1)",
        "D": "(2x-5)(x+√5)"
      },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Factor: a³ + b³ + c³ - 3abc 🔷",
      "options": {
        "A": "(a+b+c)(a²+b²+c²-ab-bc-ca)",
        "B": "1/2(a+b+c)[(a-b)²+(b-c)²+(c-a)²]",
        "C": "(a+b+c)³-3abc",
        "D": "(a+b)(b+c)(c+a)"
      },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Factorize: x² + 1/x² + 2 - 3x - 3/x 🧮",
      "options": {
        "A": "(x+1/x-1)(x+1/x-2)",
        "B": "(x²+1)/x²+2-3(x+1/x)",
        "C": "(x+1/x)²-3(x+1/x)+2",
        "D": "(x-1)(x-2)"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Factor: (x² - 3x)² - 8(x² - 3x) + 12 🚀",
      "options": {
        "A": "(x²-3x-6)(x²-3x-2)",
        "B": "(x²-3x-4)(x²-3x-3)",
        "C": "(x²-3x-12)(x²-3x+1)",
        "D": "(x²-3x-1)(x²-3x-12)"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Factorize: a⁴ + a²b² + b⁴ (similar to a⁴+4b⁴) 🌟",
      "options": {
        "A": "(a²+ab+b²)(a²-ab+b²)",
        "B": "(a²+b²)²",
        "C": "(a+b)⁴",
        "D": "(a-b)⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "Factor: x³ + y³ + z³ - 3xyz if x+y+z=0 ⚡",
      "options": {
        "A": "3xyz",
        "B": "0",
        "C": "(x+y+z)(something)",
        "D": "Cannot factor"
      },
      "correct_answer": "B"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Factorize: 12(x² + 7x)² - 8(x² + 7x)(2x-1) - 15(2x-1)² 📐",
      "options": {
        "A": "[2(x²+7x)-3(2x-1)][6(x²+7x)+5(2x-1)]",
        "B": "(x²+7x)(2x-1)",
        "C": "(2x-1)²",
        "D": "(x²+7x)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "Factor: (a-b)³ + (b-c)³ + (c-a)³ 🎯",
      "options": {
        "A": "3(a-b)(b-c)(c-a)",
        "B": "0",
        "C": "Depends on values",
        "D": "Cannot factor"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Factorize: x⁵ + x⁴ + x³ + x² + x + 1 🐍",
      "options": {
        "A": "(x+1)(x²+x+1)(x²-x+1)",
        "B": "(x³+1)(x²+x+1)",
        "C": "(x+1)(x⁴+x²+1)",
        "D": "x(x⁴+1)+1"
      },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Factor: a²(b+c) + b²(c+a) + c²(a+b) + 3abc 🔄",
      "options": {
        "A": "(a+b)(b+c)(c+a)",
        "B": "(a+b+c)(a²+b²+c²)",
        "C": "(ab+bc+ca)²",
        "D": "a²b+b²c+c²a"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Factorize: x⁴ + 4y⁴ (classic problem) ✅",
      "options": {
        "A": "(x²+2y²+2xy)(x²+2y²-2xy)",
        "B": "(x²+2y²)²-(2xy)²",
        "C": "(x+2y)(x-2y)(x²+4y²)",
        "D": "(x²+4y²)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Factor: √2 x² + 3x + √2 🧠",
      "options": {
        "A": "(√2x+1)(x+√2)",
        "B": "(√2x+√2)(x+1)",
        "C": "√2(x²+ (3/√2)x +1)",
        "D": "Not factorable"
      },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Factorize: x⁷ + x⁵ + x³ + x (take common factor first) ➗",
      "options": {
        "A": "x(x²+1)(x⁴+1)",
        "B": "x(x⁶+1)",
        "C": "x(x³+1)(x³-1)",
        "D": "x⁷+x"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Factor: a³(b-c) + b³(c-a) + c³(a-b) 🏁",
      "options": {
        "A": "(a-b)(b-c)(c-a)(a+b+c)",
        "B": "0",
        "C": "Symmetric factorization",
        "D": "Both A & C"
      },
      "correct_answer": "A"
    }
  ]
}