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Step-by-step Solution

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

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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 $\frac{\left(1-x^2\right)^2}{x^2+2x+1}$ is perfect square, 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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Answer

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

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Time to solve it:

~ 0.84 seconds

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