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

Formula

(a - b)2 = a2 - 2ab + b2

The middle sign in (a - b)2 is minus.
So the middle term of the right side, -2ab, is also minus.
This is the difference between
the (a - b)2 formula and the (a + b)2 formula.

Example

Example

Solution

First square the first term: x2.

The middle sign in (x - 7)2 is minus.
So write
-2 times,
the first term, x times,
the last term, 7.

Square the last term: +72.

So (x - 7)2 = x2 - 2⋅x⋅7 + 72.

-2⋅x⋅7 = -14x
+72 = +49

So x2 - 14x + 49 is the answer.