Category: Algebra
"Published in Newark, California, USA"
Find the factor:
(x + 2y)3 - (x3 + 8y3) = 0
Solution:
If you notice that the second group is a sum of two cubes. We can factor the second group as follows
(x + 2y)3 - (x3 + 8y3) = 0
(x + 2y)3 - (x + 2y)(x2 - 2xy + 4y2) = 0
Take out (x + 2y) as their common factor in the above equation
(x + 2y)[(x + 2y)2 - (x2 - 2xy + 4y2)] = 0
If you expand and simplify the second group, x2 and y2 will be cancel
(x + 2y)[x2 + 4xy +4y2 - x2 + 2xy - 4y2] = 0
(x + 2y)(6xy) = 0
Therefore, the answer is (x + 2y)(6xy) = 0
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