Factoring the Sum or Difference of Cubes - LAVC Math Department

Factoring Practice (Step by Step) - Sum and Difference of Cubea 3 + b 3 = (a + b) (a 2 – ab + b 2 ) and a 3 – b 3 = (a – b) (a 2 + ab + b 2 )If the cubic root of “a” and “b” can be found, then we use this method.The first parenthesis is ( 3 a 3 ± 3 b 3 ) = (a ± b) and the second parenthesis is (a 2 ± ab + b 2 ) =square of the first term, product of (-1)(a)(b) and square of the last termExample – 1: Factor x 3 + 273a = 3 x 3 = x ; 3 b = 3 27 = 3 3 3 = 3 ⇒ x 3 + 27 = x 3 + 3 3 = (x + 3) (x 2 – 3x + 9)Example – 2: 8x 3 – 1253a = 3 8x 3 = 2x ; 3 b = 3 125 = 5 ⇒ 8x 3 – 125 = (2x) 3 – 5 3 = (2x – 5) (4x 2 + 10x + 25)Factor:1) x 3 + 64 2) x 3 + 273) x 3 + 216 4) x 3 + u 35) 8x 3 + 125u 3 6) 8x 3 + 17) x 3u + 27y 3b 8) x 12 + m 129) 8y 3 + (w + 1) 3 10) 27x 3 + (y – 2) 311) x 3 – 1 12) x 3 – 2713) x 3 – 64 14) 27x 3 – 815) 8x 3 – 27 16) x 3u – 125 y 3b17) 64u 4 – u 18) (y + 8) 3 – 819) 2x 4 y 2 – 250xy 5 20) 7x 3 – 5103y 3Page 1 of 2

Factoring Practice (Step by Step) - Sum and Difference of CubeAnswers1) (x + 4) (x 2 – 4x + 16) 2) (x + 3) (x 2 – 3x + 9)3) (x + 6) (x 2 – 6x + 36) 4) (x + u) (x 2 – xu + u 2 )5) (2x + 5u) (4x 2 – 10ux + 25u 2 ) 6) (2x + 1) (4x 2 – 2x + 1)7) (x u + 3y b ) (x 2u – 3x u y b + 9y 2b ) 8) (x 4 + m 4 ) (x 8 – x 4 m 4 + m 8 )9) (2y + w + 1) [4y 2 – 2y(w + 1) + (w + 1) 2 ] 10) (3x + y – 2) [9x 2 – 3x(y – 2) + (y – 2) 2 ]11) (x – 1) (x 2 + x + 1) 12) (x – 3) (x 2 + 3x + 9)13) (x – 4) (x 2 + 4x + 16) 14) (3x – 2) (9x 2 + 6x + 4)15) (2x – 3) (4x 2 + 6x + 9) 16) (x u – 5y b ) [x 2u + 5x u y b + 25y 2b ]17) u (4u – 1)(16u 2 + 4u + 1) 18) (y + 6) (y 2 + 18y + 84)19) 2xy 2 (x – 5y) (x 2 + 5xy + 25y 2 ) 20) 7(x – 9y)(x 2 + 9x y + 81y 2 )Page 2 of 2