How do you multiply $(x + 1)(x - 1)^2$ ?

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Answer 1 · 2018-06-23T12:22:33

$(x+1)(x-1)^2=x^3-x^2-x+1$

Let's focus on $(x-1)^2$ first. This is equivalent to $(x-1)(x-1)$ . So,

$(x-1)(x-1)=x^2-x-x+1$
$(x-1)(x-1)=x^2-2x+1$

Now multiply this result by $(x+1)$ and expand:

$(x+1)(x^2-2x+1)$
$(x+1)(x^2-2x+1)=x^3-2x^2+x+x^2-2x+1$
$(x+1)(x^2-2x+1)=x^3-x^2-x+1$

How do you multiply (x + 1)(x - 1)^2(x + 1)(x - 1)^2?