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← Special Products of Polynomials

Rule

Product of a Conjugate Pair of Binomials

The product of two conjugate binomials is the difference of two squares.

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

Proof

This identity can be proved by using the Distributive Property to multiply the binomials.

(a + b)(a - b)

Distribute (a-b)

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

Distribute a

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

Distribute b

a^2-ab+ba-b^2

CommutativePropMult

Commutative Property of Multiplication

a^2-ab+ab-b^2

Add terms

a^2 - b^2

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

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