Step-by-step Solution

Simplify the expression $\frac{\left(1-x^2\right)^2}{x^2+2x+1}$

Go!
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Final Answer

$\left(1-x\right)^2$

Step-by-step explanation

Problem to solve:

$\frac{\left(1-x^2\right)^2}{x^2+2x+1}$
1

The trinomial $x^2+2x+1$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$
2

Using the perfect square trinomial formula

$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{x^2}\:and\:b=\sqrt{1}$
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Factoring the perfect square trinomial

$\frac{\left(1-x^2\right)^2}{\left(x+1\right)^{2}}$
4

Factor the difference of squares $\left(1-x^2\right)$ as the product of two conjugated binomials

$\frac{\left(1+x\right)^2\left(1-x\right)^2}{\left(x+1\right)^{2}}$
5

Simplify the fraction $\frac{\left(1+x\right)^2\left(1-x\right)^2}{\left(x+1\right)^{2}}$ by $\left(1+x\right)^2$

$\left(1-x\right)^2$

Final Answer

$\left(1-x\right)^2$