Section A:
1) x² - 6x + 12 = (x - 3)² + 3
2) 6(x - 5) - 84 = 6(x - 19)
3) b² + 2(b - 4) = (b + 1)² - 9
4) x² - 3(2x + 9) = (x - 3)² - 36
5) c(c + 8) - 48 = (c + 12)(c - 4)
6) 3a(a - 2) - 4a + 3 = (3a - 1)(a - 3)
7) 5w(w - 2) - 4w - 3 = (5w + 1)(w - 3)
8) 3(6 - 5n) + n² + n² = 2(n - 3)(n - 6)
9) 3 + 2y(4y + 5) = (2y + 1)(2y + 3)
10) 9x² - (x - 3)² = 4(2x - 1)(x + 3)
Section B:
1) x² - 4 = (x - 2)(x + 2)
2) a² - 25 = (a - 5)(a + 5)
3) t² - 64 = (t - 8)(t + 8)
4) y² - 9 = (y - 3)(y + 3)
5) 49 - p² = (7 - p)(7 + p)
6) 4q² - 121 = (2q - 11)(2q + 11)
7) 81 - 25k² = (9 - 5k)(9 + 5k)
8) 1 - 400d² = (1 - 20d)(1 + 20d)
9) 600v² - 6 = 6(10v - 1)(10v + 1)
10) a² - b² = (a - b)(a + b)
11) x² - 9y² = (x - 3y)(x + 3y)
12) 4n² - d² = (2n - d)(2n + d)
13) 16s² - 9t² = (4s - 3t)(4s + 3t)
14) 49w² - 100v² = (7w - 10v)(7w + 10v)
15) 32p² - 18q² = 2(4p - 3q)(4p + 3q)
16) 48x² - 12y² = 12(2x - y)(2x + y)
17) 45a² - 125b² = 5(3a - 5b)(3a + 5b)
18) 72x² - 242y² = 2(6x - 11y)(6x + 11y)
19) a²b² - c² = (ab - c)(ab + c)
20) 9s - 4s³ = s(3 - 2s)(3 + 2s)
21) (xy)² - 4z² = (xy - 2z)(xy + 2z)
22) 64r² - 16s⁴ = 16(2r - s²)(2r + s²)
23) (4w)² - 36y² = 4(2w - 3y)(2w + 3y)
24) 27a² - 12b² = 3(3a - 2b)(3a + 2b)
Extension:
1) 4x² - (x - 2)² = (x + 2)(3x - 2)
2) (2x + 1)² - (x - 4)² = 3(x + 5)(x - 1)
Parent Tip: Review the logic above to help your child master the concept of factorize worksheet.
