Special Product: Difference of Squares

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Difference of Squares

A difference of squares has the form (a^2-b^2). It factors into two binomials: [ a^2-b^2=(a-b)(a+b) ] This pattern is useful because it turns a subtraction of perfect squares into a product.

1) Recognize the pattern

Check whether the expression is:

a subtraction, not addition;
two perfect squares;
written as one square minus another square.

Examples: (x^2-9), (25y^2-4), (16m^4-n^2).

2) Write each square root

Find the square root of each term:

(x^2) becomes (x)
(9) becomes (3)
(25y^2) becomes (5y)

3) Build the factors

Place the same two terms in parentheses, changing only the sign: [ a^2-b^2=(a-b)(a+b) ] So, for example: [ x^2-9=(x-3)(x+3) ]

4) Check your answer

Expand mentally or by FOIL to see if the product returns the original expression. The middle terms should cancel, leaving only the difference of squares.

If the expression has a common factor first, factor that out before using this pattern.