Factorize the following expressions:
8x3 – 27y3
The above equation can be simplified as
= (2x)3 – (3y)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 = 2x and b = 3y
⇒ (2x)3 – (3y)3 = (2x – 3y)((2x)2 + (2x)(3y) + (3y)2)
= (2x – 3y)(4x2 + 6xy + 9y2)
8x3 – 27y3 = (2x – 3y)(4x2 + 6xy + 9y2)
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