{
  "title": "Identities a² – b², (a + b)², (a – b)² - Grade 8 CBSE",
  "total_questions": 60,
  "questions": [

    {"id": 1, "difficulty": "easy", "question": "What is (a + b)² equal to?", "options": {"A": "a² + 2ab + b²", "B": "a² - b²", "C": "a² - 2ab + b²", "D": "2a² + b²"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is (a - b)² equal to?", "options": {"A": "a² + b²", "B": "a² - 2ab + b²", "C": "a² + 2ab + b²", "D": "a² - b²"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "a² - b² is equal to:", "options": {"A": "(a - b)²", "B": "(a + b)(a - b)", "C": "(a + b)²", "D": "a² + 2ab + b²"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Expand: (a + b)²", "options": {"A": "a² + 2ab + b²", "B": "a² - b²", "C": "a² - 2ab + b²", "D": "a² + ab + b²"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "Expand: (a - b)²", "options": {"A": "a² + 2ab + b²", "B": "a² - 2ab + b²", "C": "a² - b²", "D": "a² + ab + b²"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Which identity is used to expand (a + b)(a - b)?", "options": {"A": "(a + b)²", "B": "(a - b)²", "C": "a² - b²", "D": "a² + 2ab"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Expand: a² - b²", "options": {"A": "(a + b)(a - b)", "B": "(a + b)²", "C": "(a - b)²", "D": "a² + b²"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Which is a perfect square identity?", "options": {"A": "a² - b²", "B": "(a + b)²", "C": "(a × b)", "D": "a² + b²"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Which represents a difference of squares?", "options": {"A": "(a + b)²", "B": "(a - b)²", "C": "a² - b²", "D": "(a + b)(a + b)"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Expand: (x + 3)²", "options": {"A": "x² + 6x + 9", "B": "x² - 6x + 9", "C": "x² - 9", "D": "x² + 3x"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Expand: (x - 4)²", "options": {"A": "x² - 8x + 16", "B": "x² + 8x + 16", "C": "x² - 16", "D": "x² + 4x"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Expand: x² - 9", "options": {"A": "(x + 3)(x - 3)", "B": "(x + 9)(x - 9)", "C": "(x - 3)²", "D": "(x + 3)²"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "Which one is (a + b)²?", "options": {"A": "a² + b²", "B": "a² + 2ab + b²", "C": "a² - b²", "D": "a² − 2ab + b²"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Expand: (2 + 5)²", "options": {"A": "14", "B": "49", "C": "25", "D": "36"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Expand: (7 - 2)²", "options": {"A": "49", "B": "25", "C": "9", "D": "16"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Use identity: 8² - 3² = ?", "options": {"A": "64", "B": "55", "C": "49", "D": "72"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "Which identity helps expand (x + y)(x - y)?", "options": {"A": "(x + y)²", "B": "(x - y)²", "C": "x² - y²", "D": "(xy)²"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Expand: (3 + x)²", "options": {"A": "x² + 6x + 9", "B": "x² - 6x + 9", "C": "x² - 9", "D": "3x + 9"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "What is (x - 5)²?", "options": {"A": "x² - 10x + 25", "B": "x² + 10x + 25", "C": "x² - 25", "D": "x² - 5x"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Factorize: a² - 16", "options": {"A": "(a - 4)(a + 4)", "B": "(a - 16)(a + 16)", "C": "(a + 4)²", "D": "(a - 4)²"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Expand: (m + n)²", "options": {"A": "m² + 2mn + n²", "B": "m² - 2mn + n²", "C": "m² - n²", "D": "2m² + n²"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Expand: (p - q)²", "options": {"A": "p² + 2pq + q²", "B": "p² - 2pq + q²", "C": "p² - q²", "D": "p² + pq"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Expand: p² - q²", "options": {"A": "(p + q)(p - q)", "B": "(p - q)²", "C": "(p + q)²", "D": "p² + 2pq + q²"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Expand: (x + 7)²", "options": {"A": "x² + 49", "B": "x² + 14x + 49", "C": "x² - 14x + 49", "D": "x² + 7x"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "Expand: (x - 9)²", "options": {"A": "x² - 18x + 81", "B": "x² + 18x + 81", "C": "x² - 81", "D": "x² + 9"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Factorize: y² - 49", "options": {"A": "(y - 7)(y + 7)", "B": "(y - 49)(y + 49)", "C": "(y - 7)²", "D": "(y + 7)²"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Expand: (2x + 3)²", "options": {"A": "4x² + 12x + 9", "B": "4x² - 12x + 9", "C": "4x² - 9", "D": "4x² + 3x + 9"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Expand: (3x - 4)²", "options": {"A": "9x² - 24x + 16", "B": "9x² + 24x + 16", "C": "9x² - 16", "D": "9x² - 12x + 16"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Factorize: 36x² - 25", "options": {"A": "(6x - 5)(6x + 5)", "B": "(6x + 5)²", "C": "(6x - 5)²", "D": "(36x - 25)(36x + 25)"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Expand: (4 + x)(4 - x)", "options": {"A": "x² - 16", "B": "16 - x²", "C": "4x² - 4", "D": "x² - 4"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Expand: (5 - y)²", "options": {"A": "25 - 10y + y²", "B": "25 + 10y + y²", "C": "y² - 25", "D": "y² - 10y"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Expand: (x + 11)²", "options": {"A": "x² + 22x + 121", "B": "x² - 22x + 121", "C": "x² + 11x + 121", "D": "x² - 121"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Factorize: m² - 100", "options": {"A": "(m - 10)(m + 10)", "B": "(m + 100)(m - 100)", "C": "(m - 10)²", "D": "(m + 10)²"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Expand: (a - 6)²", "options": {"A": "a² - 12a + 36", "B": "a² + 12a + 36", "C": "a² - 36", "D": "a² - 6a"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Expand: (a + 8)²", "options": {"A": "a² + 16a + 64", "B": "a² - 16a + 64", "C": "a² + 8a + 64", "D": "a² - 64"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Factorize: x² - 64", "options": {"A": "(x - 8)(x + 8)", "B": "(x - 64)(x + 64)", "C": "(x - 8)²", "D": "(x + 8)²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Expand: (2x - 7)²", "options": {"A": "4x² - 28x + 49", "B": "4x² + 28x + 49", "C": "4x² - 49", "D": "4x² - 7x"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Expand: (3x + 2)²", "options": {"A": "9x² + 12x + 4", "B": "9x² - 12x + 4", "C": "9x² - 4", "D": "9x² + 2x"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Factorize: 121 - y²", "options": {"A": "(11 - y)(11 + y)", "B": "(11 - y)²", "C": "(11 + y)²", "D": "(y - 11)(y + 11)"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Expand using identity: (x - 12)²", "options": {"A": "x² - 24x + 144", "B": "x² + 24x + 144", "C": "x² - 144", "D": "x² - 12x"}, "correct_answer": "A"},

    {"id": 41, "difficulty": "hard", "question": "Expand: (3a + 4b)²", "options": {"A": "9a² + 24ab + 16b²", "B": "9a² - 24ab + 16b²", "C": "9a² + 16b²", "D": "3a² + 4b²"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Expand: (5x - 2y)²", "options": {"A": "25x² - 20xy + 4y²", "B": "25x² + 20xy + 4y²", "C": "25x² - 4y²", "D": "20x² - 4y²"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "Expand: (x + 2y)(x - 2y)", "options": {"A": "x² - 4y²", "B": "x² + 4xy + 4y²", "C": "x² - 4xy + 4y²", "D": "4xy"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "Expand: (7p - 3q)²", "options": {"A": "49p² - 42pq + 9q²", "B": "49p² + 42pq + 9q²", "C": "49p² - 9q²", "D": "49p² + 21pq"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "hard", "question": "Expand using identity: (9a + b)²", "options": {"A": "81a² + 18ab + b²", "B": "81a² - 18ab + b²", "C": "81a² + b²", "D": "9a² + b²"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Expand: (4x - 5y)²", "options": {"A": "16x² - 40xy + 25y²", "B": "16x² + 40xy + 25y²", "C": "16x² - 25y²", "D": "8x² - 5y²"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Factorize: 49a² - 36b²", "options": {"A": "(7a - 6b)(7a + 6b)", "B": "(7a - 6b)²", "C": "(7a + 6b)²", "D": "(49a - 36b)(49a + 36b)"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "Expand: (x + 4y)²", "options": {"A": "x² + 8xy + 16y²", "B": "x² - 8xy + 16y²", "C": "x² + 4xy + 16y²", "D": "x² - 4xy + 16y²"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "Factorize: 81x² - 25y²", "options": {"A": "(9x - 5y)(9x + 5y)", "B": "(9x + 5y)²", "C": "(9x - 5y)²", "D": "81x² - 25y²"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "Expand: (6x + y)²", "options": {"A": "36x² + 12xy + y²", "B": "36x² - 12xy + y²", "C": "36x² + y²", "D": "6x² + y²"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "Expand: (8a - 3b)²", "options": {"A": "64a² - 48ab + 9b²", "B": "64a² + 48ab + 9b²", "C": "64a² - 9b²", "D": "8a² - 3b²"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Expand: (2a + 5b)²", "options": {"A": "4a² + 20ab + 25b²", "B": "4a² - 20ab + 25b²", "C": "4a² + 25b²", "D": "2a² + 5b²"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "Factorize: 144m² - n²", "options": {"A": "(12m - n)(12m + n)", "B": "(12m - n)²", "C": "(12m + n)²", "D": "144( m² - n² )"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "Expand: (x - 3y)²", "options": {"A": "x² - 6xy + 9y²", "B": "x² + 6xy + 9y²", "C": "x² - 9y²", "D": "x² - 3xy"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Factorize: 400p² - q²", "options": {"A": "(20p - q)(20p + q)", "B": "(20p + q)²", "C": "(20p - q)²", "D": "400( p² - q² )"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Expand: (9x - y)²", "options": {"A": "81x² - 18xy + y²", "B": "81x² + 18xy + y²", "C": "81x² - y²", "D": "9x² - y²"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Expand: (7x + 2y)²", "options": {"A": "49x² + 28xy + 4y²", "B": "49x² - 28xy + 4y²", "C": "49x² + 4y²", "D": "7x² + 2y²"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Factorize: 225a² - 64b²", "options": {"A": "(15a - 8b)(15a + 8b)", "B": "(15a - 8b)²", "C": "(15a + 8b)²", "D": "225a² + 64b²"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "Expand: (4a + 9b)²", "options": {"A": "16a² + 72ab + 81b²", "B": "16a² - 72ab + 81b²", "C": "16a² + 81b²", "D": "4a² + 9b²"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Factorize: 169 - x²", "options": {"A": "(13 - x)(13 + x)", "B": "(13 + x)²", "C": "(13 - x)²", "D": "(x - 13)(x + 13)"}, "correct_answer": "A"}

  ]
}