Simplify the expression $\frac{27m^3-125n^3}{3m-5n}$

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Final answer to the problem

$\frac{\left(3m+5n\right)\left(9m^{2}-15mn+25n^{2}\right)}{3m-5n}$
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Step-by-step Solution

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

$\frac{\left(\sqrt[3]{27m^3}+\sqrt[3]{125n^3}\right)\left(\sqrt[3]{\left(27m^3\right)^{2}}-\sqrt[3]{27m^3}\sqrt[3]{125n^3}+\sqrt[3]{\left(125n^3\right)^{2}}\right)}{3m-5n}$

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

$\frac{\left(\sqrt[3]{27m^3}+\sqrt[3]{125n^3}\right)\left(\sqrt[3]{\left(27m^3\right)^{2}}-\sqrt[3]{27m^3}\sqrt[3]{125n^3}+\sqrt[3]{\left(125n^3\right)^{2}}\right)}{3m-5n}$

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Learn how to solve polynomial long division problems step by step online. Simplify the expression (27m^3-125n^3)/(3m-5n). 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]{27}. The power of a product is equal to the product of it's factors raised to the same power.

Final answer to the problem

$\frac{\left(3m+5n\right)\left(9m^{2}-15mn+25n^{2}\right)}{3m-5n}$

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Plotting: $\frac{\left(3m+5n\right)\left(9m^{2}-15mn+25n^{2}\right)}{3m-5n}$

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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.

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