FACTORING SUMS and DIFFERENCES of CUBES

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Presentation transcript:

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

ANSWERS : x3 + 125 x3 – 125 27x3 + 8 27x3 – 8 x3 + y3 x3 – y3 4x2 + 12x + 9 16x2 – 40x + 25 49x2 - 16 1) Multiply in groups. (x + 5)(x2 – 5x + 25) (x – 5)(x2 + 5x + 25) (3x + 2)(9x2 – 6x + 4) (3x – 2)(9x2 + 6x + 4) (x + y)(x2 – xy + y2) (x – y)(x2 + xy + y2) (2x + 3)2 (4x – 5)2 (7x – 4)(7x + 4)

FIVE SPECIAL PRODUCT FORMULAS SQUARE OF A SUM (x + y)2 = x2 + 2xy + y2 SQUARE OF A DIFFERENCE (x – y)2 = x2 – 2xy + y2 DIFFERENCE OF SQUARES (x + y)(x – y) = x2 – y2 SUM OF CUBES (x + y)(x2 – xy + y2) = x3 + y3 DIFFERENCE OF CUBES (x – y)(x2 + xy + y2) = x3 – y3

2) Factor completely. a) 125x3 - 64 Solution : (5x)3 – (4)3 ( - )( + + ) 5x 4 25x2 20x 16 1st 2nd term term 1st term squared 2nd term squared product of 2 terms NOTE : Occasionally, the binomial can be factored. The trinomial can never be factored over the Real Numbers.

FACTORING SUMS and DIFFERENCES of CUBES Factor out the GCF first. b) 5p4 + 40p Answer : 5p(p + 2)(p2 – 2p + 4) c) 64x6 – 729 Answer : (2x + 3)(2x – 3)(16x4 + 36x2 + 81) d) 125 – x3 Answer : (5 – x)(25 + 5x + x2)

e) 343m3 + 64n3 ANSWER : (7m + 4n)(49m2 – 28mn + 16n2) f) 1029x3y + 24y4 ANSWER : 3y(7x + 2y)(49x2 – 14xy + 4y2)