Step 2: Write the binomial factor, then write the trinomial. Remember, a3 b3 (a b)(a2 ab b2). Square a. Product Square b. Same sign of a and b 125r3 27s3 (5r 3s)(5r)2 (5r)(3s) (3s)2 Opposite sign Step 3: Simplify: 125r3 27s3 (5r 3s)(25r2 15rs 9s2) YOU TRY 4 Factor completely. a) r3 1 b) p3 1000 c) 64x3 125y3 Just as in the other factoring problems we’ve studied so far, the fi rst step in factoring any polynomial should be to ask ourselves, “Can I factor out a GCF?” Factor 3d3 81 completely. Solution “Can I factor out a GCF?” Yes. The GCF is 3. 3d3 81 3(d3 27) Factor d 3 27. Use a3 b3 (a b)(a2 ab b2). d 3 27 (d 3)(d)2 (d )(3) (3)2 T T (d)3 (3)3 (d 3)(d 2 3d 9) 3d3 81 3(d 3 27) 3(d 3)(d2 3d 9) EXAMPLE 6 YOU TRY 5 Factor completely. a) 4t3 4 b) 72a3 9b6 As always, the fi rst thing you should do when factoring is ask yourself, “Can I factor out a GCF?” and the last thing you should do is ask yourself, “Can I factor again?” Now we will summarize the factoring methods discussed in this section. Summary Special Factoring Rules Perfect square trinomials: a2 2ab b2 (a b)2 a2 2ab b2 (a b)2 Difference of two squares: a2 b2 (a b)(a b) Sum of two cubes: a3 b3 (a b)(a2 ab b2) Difference of two cubes: a3 b3 (a b)(a2 ab b2) www.mhhe.com/messersmith SECTION 7.3 Special Factoring Techniques 385
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