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

2. ANSWERS : x
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)

3. 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

4. 2) Factor completely. a) 125x3 - 64 Solution : (5x)3 – (4)3
( )( ) 5x 4
25x2
20x 16
1st nd
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.

5. 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)

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