Question

1.

a) x^2+2xy+x+2y

b) 7x^2 -7xy-5x+5y

c) 3(x+2)-y(x+2)

d) 5(x-3)+y(3-x)

e) (x^2-8)^2+36

Answer 1

a) x² +2xy + x + 2y

= (x² +2xy) + (x + 2y)

= x(x + 2y) + (x + 2y)

= (x + 2y)(x + 1)

b) 7x² - 7xy - 5x + 5y

= (7x² - 7xy) - (5x - 5y)

= 7x(x - y) - 5(x - y)

= (x - y)(7x - 5)

c) 3(x + 2) - y(x + 2)

= (x + 2)(3 - y)

d) 5(x - 3) + y(3 - x)

= 5(x - 3) - y(x - 3)

= (x - 3)(5 - y)

e) (x² - 8)² + 36

= x⁴ - 16x² + 64 + 36

= x⁴ - 16x² + 100

= x⁴ + 20x² - 36x² + 100

= (x⁴ + 20x² + 100) - 36x²

= (x² + 10)² - (6x)²

= (x² + 10 - 6x)(x² + 10 + 6x)