{
  "title": "Factorization by Grouping - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Factorize: ax + ay + bx + by 🧩", "options": {"A": "(a + b)(x + y)", "B": "(a + x)(b + y)", "C": "a(x + y) + b", "D": "(a + y)(b + x)"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Factorize: 2m + 2n + pm + pn 🌟", "options": {"A": "(2 + p)(m + n)", "B": "2(m + n) + p", "C": "(m + n)(2p)", "D": "(2m + n)(p)"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Factorize: xy + xz + y + z 🧮", "options": {"A": "(x + 1)(y + z)", "B": "x(y + z) + 1", "C": "(y + z)(x)", "D": "(x + y)(z + 1)"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Factorize: ab + ac + b + c ✨", "options": {"A": "(a + 1)(b + c)", "B": "a(b + c) + 1", "C": "(a + b)(c + 1)", "D": "(b + c)(a)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Factorize: 3x + 3y + xz + yz 🎯", "options": {"A": "(3 + z)(x + y)", "B": "3(x + y) + z", "C": "(x + y)(3z)", "D": "(3x + z)(y)"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Factorize: pq + pr + q + r 🔢", "options": {"A": "(p + 1)(q + r)", "B": "p(q + r) + 1", "C": "(q + r)p", "D": "(p + q)(r + 1)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Factorize: 5a + 5b + ax + bx 🌈", "options": {"A": "(5 + x)(a + b)", "B": "5(a + b) + x", "C": "(a + b)(5x)", "D": "(5a + b)(x)"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Factorize: mn + mp + n + p 🧠", "options": {"A": "(m + 1)(n + p)", "B": "m(n + p) + 1", "C": "(n + p)m", "D": "(m + n)(p + 1)"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Factorize: 2x + 2y + kx + ky 📐", "options": {"A": "(2 + k)(x + y)", "B": "2(x + y) + k", "C": "(x + y)(2k)", "D": "(2x + y)(k)"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Factorize: uv + uw + v + w 🧮", "options": {"A": "(u + 1)(v + w)", "B": "u(v + w) + 1", "C": "(v + w)u", "D": "(u + v)(w + 1)"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Factorize: 4p + 4q + rp + rq 🎲", "options": {"A": "(4 + r)(p + q)", "B": "4(p + q) + r", "C": "(p + q)4r", "D": "(4p + q)(r)"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Factorize: ab + ac + db + dc 🧩", "options": {"A": "(a + d)(b + c)", "B": "a(b + c) + d", "C": "(b + c)(a + d)", "D": "(a + b)(c + d)"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Factorize: xy - xz + y - z ✨", "options": {"A": "(x + 1)(y - z)", "B": "x(y - z) + 1", "C": "(y - z)x", "D": "(x - y)(z + 1)"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Factorize: 3k + 3l + mk + ml 🔢", "options": {"A": "(3 + m)(k + l)", "B": "3(k + l) + m", "C": "(k + l)3m", "D": "(3k + l)(m)"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Factorize: ax - ay + bx - by 🎯", "options": {"A": "(a + b)(x - y)", "B": "(a - b)(x + y)", "C": "a(x - y) + b", "D": "(a + x)(b - y)"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Factorize: 2pq + 2pr + q + r 🌟", "options": {"A": "(2p + 1)(q + r)", "B": "2p(q + r) + 1", "C": "(q + r)2p", "D": "(2q + r)(p)"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Factorize: mn - mp + n - p 🧠", "options": {"A": "(m + 1)(n - p)", "B": "m(n - p) + 1", "C": "(n - p)m", "D": "(m - n)(p + 1)"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Factorize: uv - uw + v - w 📐", "options": {"A": "(u + 1)(v - w)", "B": "u(v - w) + 1", "C": "(v - w)u", "D": "(u - v)(w + 1)"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Factorize: 5x - 5y + zx - zy 🎲", "options": {"A": "(5 + z)(x - y)", "B": "5(x - y) + z", "C": "(x - y)(5z)", "D": "(5x - y)(z)"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Factorize: ab + ac - b - c 🧮", "options": {"A": "(a - 1)(b + c)", "B": "a(b + c) - 1", "C": "(b + c)(a)", "D": "(a + b)(c - 1)"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Factorize: 6xy + 9y + 4x + 6 🧩", "options": {"A": "(3y + 2)(2x + 3)", "B": "(2x + 3)(3y + 2)", "C": "(6y + 1)(x + 6)", "D": "(3x + 2)(2y + 3)"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Factorize: 2ax + 3ay + 2bx + 3by 🌟", "options": {"A": "(2x + 3y)(a + b)", "B": "(a + b)(2x + 3y)", "C": "(2a + 3b)(x + y)", "D": "(x + y)(2a + 3b)"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Factorize: pq - 2p + 3q - 6 🧮", "options": {"A": "(p + 3)(q - 2)", "B": "(p - 2)(q + 3)", "C": "(q - 2)(p + 3)", "D": "(q + 3)(p - 2)"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Factorize: 4x² + 8xy + 3x + 6y ✨", "options": {"A": "(4x + 3)(x + 2y)", "B": "(x + 2y)(4x + 3)", "C": "(2x + 3)(2x + y)", "D": "(x + 3y)(4x + 2)"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Factorize: 3a² - 6a + a - 2 🎯", "options": {"A": "(3a + 1)(a - 2)", "B": "(a - 2)(3a + 1)", "C": "(3a - 1)(a + 2)", "D": "(a + 2)(3a - 1)"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Factorize: 2mn + 3m + 4n + 6 🔢", "options": {"A": "(m + 2)(2n + 3)", "B": "(2n + 3)(m + 2)", "C": "(2m + 3)(n + 2)", "D": "(n + 2)(2m + 3)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Factorize: x²y + xy² + x + y 🌈", "options": {"A": "(xy + 1)(x + y)", "B": "(x + y)(xy + 1)", "C": "(x + 1)(y + 1)", "D": "xy(x + y) + 1"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Factorize: 5ab - 10a + 3b - 6 🧠", "options": {"A": "(5a + 3)(b - 2)", "B": "(b - 2)(5a + 3)", "C": "(5a - 3)(b + 2)", "D": "(b + 2)(5a - 3)"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Factorize: 6p²q + 9pq + 2p + 3 📐", "options": {"A": "(3pq + 1)(2p + 3)", "B": "(2p + 3)(3pq + 1)", "C": "(2pq + 1)(3p + 3)", "D": "(3p + 1)(2pq + 3)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Factorize: 2x² - 4xy + x - 2y 🎲", "options": {"A": "(2x + 1)(x - 2y)", "B": "(x - 2y)(2x + 1)", "C": "(2x - 1)(x + 2y)", "D": "(x + 2y)(2x - 1)"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Factorize: 3uv + 6u + v + 2 🧩", "options": {"A": "(3u + 1)(v + 2)", "B": "(v + 2)(3u + 1)", "C": "(u + 1)(3v + 2)", "D": "(3v + 1)(u + 2)"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Factorize: 4a²b + 6ab + 2a + 3 🌟", "options": {"A": "(2ab + 1)(2a + 3)", "B": "(2a + 3)(2ab + 1)", "C": "(ab + 1)(4a + 3)", "D": "(4a + 1)(ab + 3)"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Factorize: x³ + x² + x + 1 🧮", "options": {"A": "(x² + 1)(x + 1)", "B": "(x + 1)(x² + 1)", "C": "(x + 1)²(x - 1)", "D": "(x - 1)(x² + 1)"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Factorize: 2pq - 4p + 5q - 10 ✨", "options": {"A": "(2p + 5)(q - 2)", "B": "(q - 2)(2p + 5)", "C": "(2p - 5)(q + 2)", "D": "(q + 2)(2p - 5)"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Factorize: 3x²y - 6xy + x - 2 🎯", "options": {"A": "(3xy + 1)(x - 2)", "B": "(x - 2)(3xy + 1)", "C": "(3xy - 1)(x + 2)", "D": "(x + 2)(3xy - 1)"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Factorize: 5m² + 10m + m + 2 🔢", "options": {"A": "(5m + 1)(m + 2)", "B": "(m + 2)(5m + 1)", "C": "(5m - 1)(m - 2)", "D": "(m - 2)(5m - 1)"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Factorize: ab² + a²b + a + b 🌈", "options": {"A": "(ab + 1)(a + b)", "B": "(a + b)(ab + 1)", "C": "ab(a + b) + 1", "D": "(a + 1)(b + 1)"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Factorize: 4x³ + 8x² + x + 2 🧠", "options": {"A": "(4x² + 1)(x + 2)", "B": "(x + 2)(4x² + 1)", "C": "(2x² + 1)(2x + 2)", "D": "(x + 1)(4x² + 2)"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Factorize: 6a - 9b + 4ac - 6bc 📐", "options": {"A": "(3 + 2c)(2a - 3b)", "B": "(2a - 3b)(3 + 2c)", "C": "(2a + 3b)(3 - 2c)", "D": "(3 - 2c)(2a + 3b)"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Factorize: x² - xy + 2x - 2y 🎲", "options": {"A": "(x + 2)(x - y)", "B": "(x - y)(x + 2)", "C": "(x - 2)(x + y)", "D": "(x + y)(x - 2)"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Factorize: 2a²b + 3ab² + 4a + 6b 🧩", "options": {"A": "(ab + 2)(2a + 3b)", "B": "(2a + 3b)(ab + 2)", "C": "(a + 2b)(2ab + 3)", "D": "(2ab + 3)(a + 2b)"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Factorize: 6x³ + 9x²y + 4x + 6y 🌟", "options": {"A": "(3x² + 2)(2x + 3y)", "B": "(2x + 3y)(3x² + 2)", "C": "(2x² + 3)(3x + 2y)", "D": "(3x + 2y)(2x² + 3)"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Factorize: 4p²q - 8pq + p - 2 🧮", "options": {"A": "(4pq + 1)(p - 2)", "B": "(p - 2)(4pq + 1)", "C": "(4pq - 1)(p + 2)", "D": "(p + 2)(4pq - 1)"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Factorize: 3a³ - 6a² + a - 2 ✨", "options": {"A": "(3a² + 1)(a - 2)", "B": "(a - 2)(3a² + 1)", "C": "(3a² - 1)(a + 2)", "D": "(a + 2)(3a² - 1)"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "Factorize: x⁴ + x³ + x + 1 🎯", "options": {"A": "(x³ + 1)(x + 1)", "B": "(x + 1)(x³ + 1)", "C": "(x² + 1)(x² + 1)", "D": "(x - 1)(x³ - 1)"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Factorize: 5m²n + 10mn + 2m + 4 🔢", "options": {"A": "(5mn + 2)(m + 2)", "B": "(m + 2)(5mn + 2)", "C": "(5mn - 2)(m - 2)", "D": "(m - 2)(5mn - 2)"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Factorize: 2ab² - 4ab + 3b - 6 🌈", "options": {"A": "(2ab + 3)(b - 2)", "B": "(b - 2)(2ab + 3)", "C": "(2ab - 3)(b + 2)", "D": "(b + 2)(2ab - 3)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Factorize: 6x²y² + 9xy² + 4x + 6 🧠", "options": {"A": "(3xy² + 2)(2x + 3)", "B": "(2x + 3)(3xy² + 2)", "C": "(2xy² + 3)(3x + 2)", "D": "(3x + 2)(2xy² + 3)"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "Factorize: a³b + a²b² + a² + ab 📐", "options": {"A": "a(a + b)(ab + 1)", "B": "ab(a + 1)(a + b)", "C": "(a² + b)(ab + a)", "D": "a²b(a + b) + 1"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Factorize: 4p³ + 8p²q + p + 2q 🎲", "options": {"A": "(4p² + 1)(p + 2q)", "B": "(p + 2q)(4p² + 1)", "C": "(2p² + 1)(2p + 2q)", "D": "(p + q)(4p² + 2)"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "Factorize: 3x² - 6xy + 2x - 4y 🧩", "options": {"A": "(3x + 2)(x - 2y)", "B": "(x - 2y)(3x + 2)", "C": "(3x - 2)(x + 2y)", "D": "(x + 2y)(3x - 2)"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Factorize: 5a²b - 10ab + 3a - 6 🌟", "options": {"A": "(5ab + 3)(a - 2)", "B": "(a - 2)(5ab + 3)", "C": "(5ab - 3)(a + 2)", "D": "(a + 2)(5ab - 3)"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Factorize: 2m³ + 4m²n + m + 2n 🧮", "options": {"A": "(2m² + 1)(m + 2n)", "B": "(m + 2n)(2m² + 1)", "C": "(m² + 1)(2m + 2n)", "D": "(m + n)(2m² + 2)"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Factorize: x²y² + xy³ + x² + xy ✨", "options": {"A": "xy(x + y)(y + 1)", "B": "x(x + y)(y² + 1)", "C": "y(x + y)(x² + 1)", "D": "xy(x + y) + x²"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Factorize: 6p² - 9pq + 4p - 6q 🎯", "options": {"A": "(3p + 2)(2p - 3q)", "B": "(2p - 3q)(3p + 2)", "C": "(3p - 2)(2p + 3q)", "D": "(2p + 3q)(3p - 2)"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Factorize: a³ + a²b + a + b 🔢", "options": {"A": "(a² + 1)(a + b)", "B": "(a + b)(a² + 1)", "C": "a²(a + b) + 1", "D": "(a + 1)(a² + b)"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Factorize: 4x³y + 6x²y + 2x + 3 🌈", "options": {"A": "(2x²y + 1)(2x + 3)", "B": "(2x + 3)(2x²y + 1)", "C": "(x²y + 1)(4x + 3)", "D": "(4x + 1)(x²y + 3)"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Factorize: 3u²v - 6uv + u - 2 🧠", "options": {"A": "(3uv + 1)(u - 2)", "B": "(u - 2)(3uv + 1)", "C": "(3uv - 1)(u + 2)", "D": "(u + 2)(3uv - 1)"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Factorize: 2a² + 4ab + a + 2b 📐", "options": {"A": "(2a + 1)(a + 2b)", "B": "(a + 2b)(2a + 1)", "C": "(2a - 1)(a - 2b)", "D": "(a - 2b)(2a - 1)"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Factorize: x³y + x²y² + xy + y² 🎲", "options": {"A": "y(x² + y)(x + 1)", "B": "xy(x + y)(x + 1)", "C": "x²y(x + y) + y", "D": "y²(x² + x + 1)"}, "correct_answer": "A"}
  ]
}