Question

Answer 1

`a, a(x+y) - b(x+y)`

`= (a-b)(x+y)`

`b, x(x-y) + 7(x-y)`

`= (x+7)(x-y)`

`c,x(x-8) - y(x-8)`

`= (x-y)(x-8)`

Answer 2

a) ax + ay - bx - by

= (ax + ay) + (-bx - by)

= a(x + y) - b(x + y)

= (x + y)(a - b)

b) x² - xy + 7x - 7y

= (x² - xy) + (7x - 7y)

= x(x - y) + 7(x - y)

= (x - y)(x + 7)

c) x² - 8x - xy + 8y

= (x² - 8x) + (-xy + 8y)

= x(x - 8) - y(x - 8)

= (x - 8)(x - y)

e) x² - 2xy - 1 + y²

= (x² - 2xy + y²) - 1

= (x - y)² - 1²

= (x - y - 1)(x - y + 1)

f) 3x⁵ - 3x³y² + 6x⁴z + 3x³z²

= 3x³(x² - y² + 2xz + z²)

= 3x³[(x² + 2xz + z²) - y²]

= 3x³[(x + z)² - y²]

= 3x³(x + z - y)(x + z + y)