How do you expand $(2x^4-1)^6$ ?

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Answer 1 · 2016-11-24T07:03:02

To make it a bit easier to view:

Let $a=2x^4 and b=-1$

Then we will have $(a+b)^6$

To start expanding, we should separate the function:

$=(a+b)(a+b)(a+b)(a+b)(a+b)(a+b)$

Then start multiplying:

$=(a^2+2ab+b^2)(a+b)(a+b)(a+b)(a+b)$

$=(a^3+2a^2b+ab^2+a^2b+2ab^2+b^3)(a+b)(a+b)(a+b)$

Repeat this process until all values are distributed (no parentheses)

You should end up with:

$64x^{24}-192x^{20}+240x^{16}-160x^{12}+60x^8-12x^4+1$

How do you expand (2x^4-1)^6(2x^4-1)^6?