Factorize the following expressions:
x3 – 8y3
The above equation can be simplified as
= (x)3 – (2y)3
Both the given terms are perfect cubes, factor using the subtraction of cubes formula,
(a)3 – (b)3 = (a – b)(a2 + ab + b2)
Here a = x and b = 2y
⇒ (x)3 – (2y)3 = (x – 2y)((x)2 + (x)(2y) + (2y)2)
= (x – y)(x2 + 2xy + 4y2)
x3 – 8y3 = (x – y)(x2 + 2xy + 4y2)
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