Simplify the expression $\frac{512a^9+b^9}{2a+b}$

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Final answer to the problem

$\frac{\left(8a^{3}+b^{3}\right)\left(64a^{6}-8a^{3}b^{3}+b^{6}\right)}{2a+b}$
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Step-by-step Solution

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  • Solve by quadratic formula (general formula)
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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$

$\frac{\left(\sqrt[3]{512a^9}+\sqrt[3]{b^9}\right)\left(\sqrt[3]{\left(512a^9\right)^{2}}-\sqrt[3]{512a^9}\sqrt[3]{b^9}+\sqrt[3]{\left(b^9\right)^{2}}\right)}{2a+b}$

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

$\frac{\left(\sqrt[3]{512a^9}+\sqrt[3]{b^9}\right)\left(\sqrt[3]{\left(512a^9\right)^{2}}-\sqrt[3]{512a^9}\sqrt[3]{b^9}+\sqrt[3]{\left(b^9\right)^{2}}\right)}{2a+b}$

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Learn how to solve polynomial long division problems step by step online. Simplify the expression (512a^9+b^9)/(2a+b). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). The power of a product is equal to the product of it's factors raised to the same power. Calculate the power \sqrt[3]{512}. The power of a product is equal to the product of it's factors raised to the same power.

Final answer to the problem

$\frac{\left(8a^{3}+b^{3}\right)\left(64a^{6}-8a^{3}b^{3}+b^{6}\right)}{2a+b}$

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Function Plot

Plotting: $\frac{\left(8a^{3}+b^{3}\right)\left(64a^{6}-8a^{3}b^{3}+b^{6}\right)}{2a+b}$

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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.

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