## Intermediate Algebra (6th Edition)

$x^{4}-4x^{3}+6x^{2}-4x+1$
$(x-1)^{4} =( (x-1)^{2}) ^{2}$ Using the formula $(a-b)^{2}= a^{2}-2ab+b^{2}$ $(x-1)^{2} = (x^{2}-2x+1)$ $=(x^{2}-2x+1)^{2}$ $=(x^{2}-2x+1)(x^{2}-2x+1)$ $=x^{4}-2x^{3}+x^{2}-2x^{3}+4x^{2}-2x+x^{2}-2x+1$ Combine like terms. $=x^{4}-2x^{3}-2x^{3}+x^{2}+4x^{2}+x^{2}-2x-2x+1$ $=x^{4}-4x^{3}+6x^{2}-4x+1$