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How do you use the Binomial Theorem to expand #(2x−1)^4#?

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Hriman Share
Apr 27, 2018

Answer:

#16x^4-32x^3+24x^2-8x+1#

Explanation:

Given: #(2x-1)^4#

We can say that:
#(2x)^4(-1)^0+(2x)^3(-1)^1+(2x)^2(-1)^2+(2x)^1(-1)^3+(2x)^0(-1)^4=#

#16x^4-8x^3+4x^2-2x+1#

However we are not quite done, we need the coefficients in front of each term, I would use combinations unless you really want to use Pascal's triangle, which you can since this a small exponent.

Using pascal's triangle:
For row 4: the coefficients are #1, 4, 6, 4, 1#

#1*16x^4+4*-8x^3+6*4x^2+4*-2x+1*1#

#16x^4-32x^3+24x^2-8x+1#

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