Step-by-step Solution

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

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Final Answer

$\left(1-x\right)^2$
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Step-by-step Solution

Problem to solve:

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

Choose the solving method

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

$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{x^2}\:and\:b=\sqrt{1}$
3

Factoring the perfect square trinomial

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

The power of a product is equal to the product of it's factors raised to the same power

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

$\left(1-x\right)^2$
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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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