Factoring Sums & Differences of Cubes

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Presentation transcript:

Factoring Sums & Differences of Cubes

Factoring Sums & Differences of Cubes Sum & Difference of Cubes: Has two terms The terms are separated by a + or – sign Each term is a perfect cube

Factoring Sums & Differences of Cubes Factors of a Sum/Difference of Cubes: a3 + b3 = (a + b)(a2 – ab + b2) a3 – b3 = (a – b)(a2 + ab + b2) Sum of Cubes Difference of Cubes

Factoring Sums & Differences of Cubes Example 1: Factor each of the following polynomials completely. s3 + t3 = (s + t)(s2 - st + t2) v3 – w3 = (v – w)(v2 + vw + w2)

Factoring Sums & Differences of Cubes Example 2: Factor each of the following polynomials completely. 8x3 – 27 = (2x – 3)((2x)2 + (2x)(3) + (3)2)  Use the pattern a3 – b3 = (a – b)(a2 + ab + b2) = (2x – 3)(4x2 + 6x + 9) b) 9x4 – 9x = 9x(x3 – 1)  First remove the GCF = 9x(x – 1)(x2 + x + 1)  Factor the difference of cubes x3 – 1

Homework Do #1 – 19  odd questions only on page 120 section 4.2 for Thursday 