# Square of a Difference (a - b)^{2}

How to solve the square of a difference (a - b)^{2}: formula, 1 example, and its solution.

## Formula

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

The middle sign in (a - b)^{2} is (-).

So the middle term of the right side, -2ab,

is also (-).

This is the difference between

the (a - b)^{2} formula and the (a + b)^{2} formula.

## Example(x - 7)^{2}

Solution

Solution (Detail)

First square the first term: x^{2}.

The middle sign in (x - 7)^{2} is (-).

So write

-2 times,

the first term, x times,

the last term, 7.

Square the last term: +7^{2}.

So (x - 7)^{2} = x^{2} - 2⋅x⋅7 + 7^{2}.

-2⋅x⋅7 = -14x

+7^{2} = +49

So

x^{2} - 14x + 49

is the answer.