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# Factoring the Difference of Two Squares

 WHAT TO DO: HOW TO DO IT: 1. Factor the binomial 49x4 − 36y4 The difference of two terms with â€œsquare coefficientsâ€and â€œeven exponentsâ€ will always be factored as the difference of squares. 49x4 − 36y4 49x4 − 36y4 (7x2 + 6y2)(7x2 − 6y2) 2. Factor the binomial x8 − y8 Sometimes the factors themselves contain a factorable binomial → difference of squares. Another difference of squares. Continue factoring: Continue factoring to prime factors: x8 − y8 x8 − y8 = (x4 + y4)(x4 − y4) = (x4 + y4)(x2 + y2)(x2 − y2) = (x4 + y4)(x2 + y2)(x + y)(x − y) 3. Factor the expression (t + 4)2 − 9 Some expressions can be factored as the â€œdifference of squaresâ€ when one of the squared terms is inside parentheses Simplify: (t + 4)2 − 9 [(t + 4) + 3][(t + 4) − 3] (t + 7) (t + 1) 4. Factor Watch for fractions in the expressions. 5. Factor completely: 16x3y − 36xy3 Factor out the common factors then note that the term in parentheses can be factored as the difference of squares. The remaining factors are â€œprimeâ€ in rational numbers. 16x3y − 36xy3 4xy(4x2 − 9y2) 4xy(2x + 3y)(2x − 3y)