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

Mbalisikerc

Mbalisikerc

Answered question

2022-07-27

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

Answer & Explanation

Mireya Hoffman

Mireya Hoffman

Beginner2022-07-28Added 14 answers

Let (a^2-ab) = x
Let b = y
Therefore,
(a^2-ab)^2 - 8b(a^2-ab) + 12b^2= x^2 - 8yx + 12y^2
= x^2 -2 (x) (4y) + 16 y^2 - 4y^2
= (x-4y)^2 - 4y^2 (Since p^2 -2pq + q^2 = (p-q)^2)
= (x-4y -2y) (x-4y+2y) (Since p^2 - q^2 = (p-q)(p+q) )
= (x-6y) (x-2y)
Substituting (a^2-ab) = x and b=y
Answer = (a^2-ab-6b)(a^2-ab-2b)

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