How do you simplify $(a+b)^3$ ?

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Answer 1 · 2018-06-28T23:18:23

$(a+b)^3$

$=(a+b)(a+b)^2$

$=(a+b)(a^2+2ab+b^2)$

$=a^3+3a^2b+3ab^2+b^3$

Answer 2 · 2018-06-28T23:20:51

$a^3+3a^2b+3ab^2+b^3$

$(a+b)^3$ is the same as $(a+b)^2(a+b)$ , so if we write it in this way, it becomes a much easier problem to solve.

$(a+b)^2$ is the same as $(a+b)(a+b)$ , and if we distribute the $a$ and $b$ to both terms, we'll get

$a^2+2ab+b^2$

We now have

$(a+b)(a^2+2ab+b^2)$

Again, we can distribute the $a$ and $b$ to all terms to get

$a^3+2a^2b+ab^2+a^2b+2ab^2+b^3$

This simplifies to

$a^3+3a^2b+3ab^2+b^3$

Hope this helps!

How do you simplify (a+b)^3(a+b)^3?