Product of a Sum and a Difference

Product of a Sum and a Difference

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

Formula

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

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

Example 1

Find the given product. (x + 2)(x - 2)

Put x and 2 into the formula.

Example 2

Find the given product. (2u + 3v)(2u - 3v)

Put 2u and 3v into the formula.

Example 3

Find the given product. 103*97

Instead of solving 103⋅97,
change this into (100 + 3)(100 - 3).

Then, by using the formula,
(100 + 3)(100 - 3) = 1002 - 32.

As you can see, by using the formula,
you can easily solve this product.

Example 4

Find the given product. (d^2 + 1)(d + 1)(d - 1)

(d + 1)(d - 1) = d2 - 12.

Use the formula once again:
(d2 + 1)(d2 - 1) = (d2)2 - 12.