Question

Fully factorise in prime factors: 1. (3x^2)(p-q) + (18x)(p-q) - (21)(p-q)

Answer 1

The expression is 3x2(p-q) + 18x(p-q) - 21(p-q).

= (p-q) [3x2 + 18x - 21]

= 3(p-q) [x2 + 6x - 7]

= 3(p-q) [x2 + 6x - 7]

= 3(p-q) [x2 + 7x - x - 7]

= 3(p-q) [x(x + 7) - 1(x + 7)]

= 3(p-q)(x - 1)(x + 7).

The factor form of 3x2(p-q) + 18x(p-q) - 21(p-q) = 3(p-q)(x - 1)(x + 7).