Factorise (i) 6ab - b 2 + 12ac - 2bc (ii) x 2 + y - xy - x (iii) x 3 - 2x 2 y + 3xy 2 - 6y 3 (iv) a(a + b - c) – bc

Question

Factorise (i) 6ab - b 2 + 12ac - 2bc (ii) x 2 + y - xy - x (iii) x 3 - 2x 2 y + 3xy 2 - 6y 3 (iv) a(a + b - c) &#x2013; bc

Philoid · Accepted Answer

(i) 6ab - b² + 12ac - 2bc
= (6ab - b²) + (12ac - 2bc)
= b(6a - b) + 2c(6a - b)
= (6a - b) (b + 2c)
(ii) x² + y - xy - x
= x² - xy - x + y
= x(x - y) - (x - y)
= (x - y) (x - 1)
(iii) x³ - 2x²y + 3xy² - 6y³
= (x³ - 2x²y) + (3xy² - 6y³)
= x²(x - 2y) + 3y²(x - 2y)
= (x - 2y) (x² + 3y²)
(iv) a(a + b - c) - bc
= a² + ab - ac - bc
= a(a + b) - c(a + b)
= (a + b) (a - c)

Factorise(i) 6ab - b2 + 12ac - 2bc(ii) x2 + y - xy - x(iii) x3 - 2x2y + 3xy2 - 6y3(iv) a(a + b - c) – bc

Factorise
(i) 6ab - b² + 12ac - 2bc
(ii) x² + y - xy - x
(iii) x³ - 2x²y + 3xy² - 6y³
(iv) a(a + b - c) – bc