Factorize the following expressions:
27x3 + 64y3
The above equation can be simplified as
= (3x)3 + (4y)3
Both the given terms are perfect cubes, factor using the sum of cubes formula,
(a)3 + (b)3 = (a + b)(a2 – ab + b2)
Here a = 3x and b = 4y
⇒ (3x)3 + (4y)3 = (3x + 4y)((3x)2 – (3x)(4y) + (4y)2)
= (3x + 4y)(9x2 – 12xy + 16y2)
27x3 + 64y3 = (3x + 4y)(9x2 – 12xy + 16y2)
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