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h2 4 is the sum of two squares. It will not factor. h2 4 is the difference of two squares, so it will factor. h2 4 T T h2 4 (h 2)(h 2) (h)2 (2)2 a h and b 2 Therefore, h4 16 (h2 4)(h2 4) (h2 4)(h 2)(h 2). YOU TRY 3 Factor completely. a) 12p4 27p2 b) y4 1 c) 2n2 72 3 Factor the Sum and Difference of Two Cubes We can understand where we get the formulas for factoring the sum and difference of two cubes by looking at two products. (a b)(a2 ab b2) a(a2 ab b2) b(a2 ab b2) Distributive property a3 a2b ab2 a2b ab2 b3 Distribute. a3 b3 Combine like terms. So, (a b)(a2 ab b2) a3 b3, the sum of two cubes. Now, let’s multiply (a b)(a2 ab b2). (a b)(a2 ab b2) a(a2 ab b2) b(a2 ab b2) Distributive property a3 a2b ab2 a2b ab2 b3 Distribute. a3 b3 Combine like terms. So, (a b)(a2 ab b2) a3 b3, the difference of two cubes. The formulas for factoring the sum and difference of two cubes, then, are as follows: Formula Factoring the Sum and Difference of Two Cubes a3 b3 (a b)(a2 ab b2) a3 b3 (a b)(a2 ab b2) Note Notice that each factorization is the product of a binomial and a trinomial. To factor the sum and difference of two cubes Step 1: Identify a and b. Step 2: Place them in the binomial factor, and write the trinomial based on a and b. Step 3: Simplify. Write down any patterns you see in the formulas. This may help you remember them. www.mhhe.com/messersmith SECTION 7.3 Special Factoring Techniques 383


messersmith_power_intermediate_algebra_1e_ch4_7_10
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