I am trying to factor the following polynomial:

Rowan Callahan

Rowan Callahan

Answered question

2022-04-01

I am trying to factor the following polynomial:
8x34x2y18xy2+9y3

Answer & Explanation

Dixie Reed

Dixie Reed

Beginner2022-04-02Added 15 answers

Look at the following factorisation, I thought of:
8x34x2y18xy2+9y3=4x2(2xy)9y2(2xy)
=(4x29y2)(2xy)
=(2x+3y)(2x3y)(2xy)
I also want to add that, it is natural to think of the cubic identity you gave us, but 9y3 doesn't look good when trying to write as a perfect cube. Also, in particular, in using any identity of this kind, intuitively, since x2y term has a negative sign, it shoud have come from coefficient of y, which means the y3 term must have had a negative coefficient, which is not the case!

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