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Step-by-step Solution

Solve 15a*(a+1)^3-5a*(a+1)^2^3^2

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Answer

$15a^{4}+15a^{3}+30a^{3}+30a^2+15a^2+15a-5a\left(a+1\right)^{12}$

Step-by-step explanation

Problem to solve:

$15a\left(a+1\right)^3-5a\left(\left(\left(a+1\right)^2\right)^3\right)^2$
1

Applying the power of a power property

$15a\left(a+1\right)^3-5a\left(a+1\right)^{12}$
2

Apply the rule of the cube of a binomial

$15a\left(a+1\right)\left(a^2+2a+1\right)-5a\left(a+1\right)^{12}$

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Answer

$15a^{4}+15a^{3}+30a^{3}+30a^2+15a^2+15a-5a\left(a+1\right)^{12}$
$15a\left(a+1\right)^3-5a\left(\left(\left(a+1\right)^2\right)^3\right)^2$

Main topic:

Polynomials

Time to solve it:

~ 0.59 seconds