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how would i factor this binomial?

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\({36x^3 - 64x}\)

i know that this is a difference of squares... but i'm not sure how can i get the textbook answer of \({4x(3x +4)(3x -4)}\)? i got \({x(6x - 8)(6x + 8)}\) isn't that the same thing? and please show step by step!

Jul 9, 2018
edited by Guest  Jul 9, 2018
edited by Guest  Jul 9, 2018
edited by Guest  Jul 9, 2018

#1
+1

Factor the following:
36 x^3 - 64 x

Factor common terms out of 36 x^3 - 64 x.
Factor 4 x out of 36 x^3 - 64 x:
4 x (9 x^2 - 16)

Express 9 x^2 - 16 as a difference of squares.
9 x^2 - 16 = (3 x)^2 - 4^2:
4 x (3 x)^2 - 4^2
Factor the difference of two squares. (3 x)^2 - 4^2 = (3 x - 4) (3 x + 4):
4 x (3 x - 4) (3 x + 4)

Jul 9, 2018
#2
+102761
+1

YES yours is the same thing BUT yours is not fully factored.

You can factor 2 out of each of the brackets and then you will get the text book answer.

Yours is not wrong, it is just not finished.

This is a good question becasue you are obviously trying to understand.

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