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

Formula

(a + b)3 = a3 + 3a2b + 3ab2 + b3

The middle sign in (a + b)3 is plus.
So the signs of the right side terms are all plus.
This is the difference between
the (a + b)3 formula and the (a - b)3 formula.

Example

Example

Solution

First cube the first term: x3.

The middle sign in (x + 2)3 is plus.
So the signs of the right side terms terms are plus.

So write
+3 times,
square the first term, x2 times,
the last term, 2.

Write
+3 times,
the first term, x times,
square the last term, 22.

And cube the last term: +23.

So (x + 2)3 = x3 + 3⋅x2⋅2 + 3⋅x⋅22 + 23.

+3⋅x2⋅2 = +6x2
+3⋅x⋅22 = +12x
+23 = +8

So x3 + 6x2 + 12x + 8 is the answer.