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

Step-by-step Solution

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Final Answer

$\left(-1+x^{4}\right)\left(\left(x^2+1\right)^2-x^2\right)\left(x^4-x^2+1\right)$
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Step-by-step Solution

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Factor the difference of squares $\left(x^4-1\right)$ as the product of two conjugated binomials

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

Learn how to solve polynomial long division problems step by step online.

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

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Learn how to solve polynomial long division problems step by step online. Simplify the expression ((x^4-x^2+1)(x^2+x+1)(x^2-x+1)(x^4-1)^2)/((x^2-1)(x^2+1)). Factor the difference of squares \left(x^4-1\right) as the product of two conjugated binomials. Simplify the fraction \frac{\left(x^4-x^2+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^{2}+1\right)^2\left(x^{2}-1\right)^2}{\left(x^2-1\right)\left(x^2+1\right)} by x^2-1. Simplify the fraction \frac{\left(x^4-x^2+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^{2}+1\right)^2\left(x^2-1\right)}{x^2+1} by x^2+1. Solve the product of difference of squares .

Final Answer

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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x^4+-1x^2)(x^2+x)/(x^2-1)(x^2+1) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

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

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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

How to improve your answer:

Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

Used Formulas

1. See formulas

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