How to factor? : (a^2-ab)^2-8b^2(a^2-ab)+12b^4

Faith Welch 2022-07-24 Answered
How to factor? : (a^2-ab)^2-8b^2(a^2-ab)+12b^4
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Answers (1)

sviudes7w
Answered 2022-07-25 Author has 12 answers
How to factor?:
(a^2-ab)^2-8b^2(a^2-ab)+12b^4
let a^2-ab= x
b^2 =y
now
x^2 - 8xy+12y^2
x^2 -6xy-2xy +12y^2
x(x-6y)-2y(x-6y)
(x-2y)(x-6y)
(a^2-ab-2b^2)(a^2-ab-6b^2)
(a^2-ab-2b^2) = a^2-2ab+ab-2b^2 = a(a-2b)+b(a-2b) = (a+b)(a-2b)
(a^2-ab-6b^2) = a^2-3ab+2ab-6b^2 = a(a-3b)+2b(a-3b) = (a+2b)(a-3b)
now
(a^2-ab)^2-8b^2(a^2-ab)+12b^4 = (a^2-ab-2b^2)(a^2-ab-6b^2) = (a+b)(a-2b)(a+2b)(a-3b) are factors

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