Rule

Product of a Conjugate Pair of Binomials

When a binomial is multiplied by its conjugate, the resulting expression is the difference of two squares.

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

This identity can be shown using the Distributive Property — multiplying each term in the first set of parentheses with each term in the second.

(a + b) (a - b)

DistrDistribute

(a + b)

a (a + b) - b (a + b)

DistrDistribute

a

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

DistrDistribute

- b

a^{2} + a b - b a - b^{2}

Simplify

CommutativePropMultCommutative Property of Multiplication

a^{2} + a b - a b - b^{2}

SubTermSubtract term

a^{2} - b^{2}

Thus, the product of a binomial and its conjugate is the difference of two squares.