# Cube of a Sum (a + b)^{3}

How to solve the cube of a sum (a + b)^{3}: formula, 1 example, and its solution.

## Formula

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

The middle sign in (a + b)^{3} is (+).

So the signs of the right side terms

are all (+).

This is the difference between

the (a + b)^{3} formula and the (a - b)^{3} formula.

## Example(x + 2)^{3}

Solution

Solution (Detail)

First cube the first term: x^{3}.

The middle sign in (x + 2)^{3} is (+).

So the signs of the right side terms

are all (+).

So write

+3 times,

square the first term, x^{2} times,

the last term, 2.

Write

+3 times,

the first term, x times,

square the last term, 2^{2}.

And cube the last term: +2^{3}.

So (x + 2)^{3}

= x^{3} + 3⋅x^{2}⋅2 + 3⋅x⋅2^{2} + 2^{3}.

+3⋅x^{2}⋅2 = +6x^{2}

+3⋅x⋅2^{2} = +12x

+2^{3} = +8

So

x^{3} + 6x^{2} + 12x + 8

is the answer.