Quick!!! Please factor the expressions

Question

Factor the following expression:

a) x⁴ – 18x² + 81

Factors these expressions fully:

a) 2x⁴ – 32

b) 81 - 25x²

Answer 1

first a or alpha) is (x^2-9)^2 = [(x+3)(x-3)]^2 = (x+3)(x+3)(x-3)(x-3) = (x+3)^2(x-3)^2

2nd a) is 2a^4-32= 2(a^4-16) = 2(a^2-4)^(a^2+4) = 2(a-2)(a+2)(a^2+4)

b) is 81-25x^2 = (9-5x)(9+5x)

they're all involve versions of the general formula: (a^2-b^2) = (a-b)(a+b)