Square of a Sum

Square of a Sum

How to solve the square of a sum problems: formula, examples, and their solutions.

Formula

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

(a + b)2 = (a + b)(a + b).

By using the FOIL method,
(a + b)(a + b) = a2 + 2ab + b2.

So (a + b)2 = a2 + 2ab + b2.

See the brown (+) signs.
The (+) sign in (a + b)2
makes the middle term (+): +2ab.

It's the difference between
this formula and (a - b)2 formula.

Example 1

Find the given product. (x + 3)^2

Put x, (+), 3 into the formula.

Example 2

Find the given product. (2m + 5n)^2

Put 2m, (+), 5n into the formula.