ALGEBRA II HONORSGIFTED FACTORING SUMS and DIFFERENCES of

ALGEBRA II HONORS/GIFTED @ FACTORING SUMS and DIFFERENCES of CUBES

1) Multiply in groups ANSWERS : a) (x + 5)(x 2 – 5 x + 25) a) x 3 + 125 b) (x – 5)(x 2 + 5 x + 25) b) x 3 – 125 c) (3 x + 2)(9 x 2 – 6 x + 4) c) 27 x 3 + 8 d) (3 x – 2)(9 x 2 + 6 x + 4) d) 27 x 3 – 8 e) (x + y)(x 2 – xy + y 2) e) x 3 + y 3 f) (x – y)(x 2 + xy + y 2) f) x 3 – y 3 g) (2 x + 3)2 g) 4 x 2 + 12 x + 9 h) (4 x – 5)2 h) 16 x 2 – 40 x + 25 i) (7 x – 4)(7 x + 4) i) 49 x 2 - 16

FIVE SPECIAL PRODUCT FORMULAS SQUARE OF A SUM (x + y)2 = x 2 + 2 xy + y 2 SQUARE OF A DIFFERENCE (x – y)2 = x 2 – 2 xy + y 2 DIFFERENCE OF SQUARES (x + y)(x – y) = x 2 – y 2 SUM OF CUBES (x + y)(x 2 – xy + y 2) = x 3 + y 3 DIFFERENCE OF CUBES (x – y)(x 2 + xy + y 2) = x 3 – y 3

2) Factor completely. a) 125 x 3 - 64 Solution : (5 x)3 – (4)3 ( 5 x - 4 )( 25 x 2 + 20 x + 16 ) 1 st term 2 nd term 1 st term squared 2 nd term squared product of 2 terms NOTE : Occasionally, the binomial can be factored. The trinomial can never be factored over the Real Numbers.

b) 5 p 4 + 40 p Answer : 5 p(p + 2)(p 2 – 2 p + 4) c) 64 x 6 – 729 Answer : (2 x + 3)(2 x – 3)(16 x 4 + 36 x 2 + 81) d) 125 – x 3 Answer : (5 – x)(25 + 5 x + x 2) Factor out the GCF first.

e) 343 m 3 + 64 n 3 ANSWER : (7 m + 4 n)(49 m 2 – 28 mn + 16 n 2) f) 1029 x 3 y + 24 y 4 ANSWER : 3 y(7 x + 2 y)(49 x 2 – 14 xy + 4 y 2)