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#