Answer
$x^4-8x^3+24x^2-32x+16$
Work Step by Step
$(x-2)^4\longrightarrow$ Rewrite as squared binomials.
$(x-2)^2(x-2)^2\longrightarrow$ Multiply using FOIL method
$[x^2-4x+4][x^2-4x+4]\longrightarrow$ Regroup to create squared binomial
$[(x^2-4x)+4]^2\longrightarrow$ Multiply using FOIL method
$(x^2-4x)^2+2(4(x^2-4x)+16\longrightarrow$ Multiply the squared binomial using FOIL method. Apply distributive method.
$x^4-8x^3+16x^2+8x^2-32x+16\longrightarrow$ Combine like terms.
$x^4-8x^3+24x^2-32x+16$
