1) (x + y)(x - y)
2) x(y - 8)(y - 1)
3) 2a(b - y)(b - x)
4) 2p(2q - p) - 2q(p - 2q) = 2p(2q - p) + 2q(2q - p) = (2q - p)(2p + 2q) = 2(2q - p)(p + q)
5) 2a(b + 5) - (5 + a) = 2ab + 10a - 5 - a = 2ab + 9a - 5 — This does not factor nicely by grouping as written. Assuming typo: 2a(b + 5) - (b + 5) = (b + 5)(2a - 1)
6) 3a + ab + 3c + bc = a(3 + b) + c(3 + b) = (3 + b)(a + c)
7) a² - 2a + ay - 2y = a(a - 2) + y(a - 2) = (a - 2)(a + y)
8) a² - 2a + ay - 2y = a(a - 2) + y(a - 2) = (a - 2)(a + y)
9) a² - 2xy + 4ax - 8yx = a² + 4ax - 2xy - 8xy = a(a + 4x) - 2xy(1 + 4) — Not standard. Assume intended: a² - 2xy + 4ax - 8xy = a² + 4ax - 10xy — doesn't group well. Perhaps typo: a² - 2ay + 4ax - 8xy = a(a - 2y) + 4x(a - 2y) = (a - 2y)(a + 4x)
10) p² - 2p² + 6p - 6 = -p² + 6p - 6 — doesn’t factor nicely by grouping. Assume typo: p² - 2p + 6p - 12 = p(p - 2) + 6(p - 2) = (p - 2)(p + 6)
11) 2a² + a² + 6a + 2 = 3a² + 6a + 2 — doesn’t factor nicely. Assume typo: 2a² + a + 6a + 3 = 2a² + 7a + 3 — or perhaps 2a² + 2a + 6a + 6 = 2a(a + 1) + 6(a + 1) = (a + 1)(2a + 6) = 2(a + 1)(a + 3)
12) p² - 2pq + qp - 2qr = p² - pq - 2qr — doesn’t group. Assume typo: p² - 2pq + qr - 2pr = p(p - 2q) - r(2p - q) — not standard. Perhaps p² - 2pq + pr - 2qr = p(p - 2q) + r(p - 2q) = (p - 2q)(p + r)
13) a² - 3ay - 6ac + 18cy = a(a - 3y) - 6c(a - 3y) = (a - 3y)(a - 6c)
14) 2xy - 2y - 12x + 6 = 2y(x - 1) - 6(2x - 1) — doesn’t group. Assume typo: 2xy - 2y - 12x + 12 = 2y(x - 1) - 12(x - 1) = (x - 1)(2y - 12) = 2(x - 1)(y - 6)
15) 2ab - 3c - 6 + 12a = 2ab + 12a - 3c - 6 = 2a(b + 6) - 3(c + 2) — doesn’t factor. Assume typo: 2ab - 3b - 6a + 9 = b(2a - 3) - 3(2a - 3) = (2a - 3)(b - 3)
Parent Tip: Review the logic above to help your child master the concept of algebra factoring worksheet.
