Answer
$x^6-12x^5+60x^4-160x^3+240x^2-192x+64$
Work Step by Step
We are given the expression:
$(x-2)^6$
Use the Binomial Theorem to expand the expression:
$(x-2)^6=\sum_{k=0}^6 \binom{6}{k}x^{6-k}(-2)^k$
$=\binom{6}{0}x^6(-2)^0+\binom{6}{1}x^5(-2)^1+\binom{6}{2}x^4(-2)^2+\binom{6}{3}x^3(-1)^3+\binom{6}{4}x^2(-1)^4+\binom{6}{5}x^1(-2)^5+\binom{6}{6}x^0(-2)^6$
$=x^6+6(-2)x^5+15(4)x^4+20(-8)x^3+15(16)x^2+6(-32)x^1+64$
$=x^6-12x^5+60x^4-160x^3+240x^2-192x+64$
