Factorize the following expressions:
a3 + 125
The above equation can be simplified as
= (a)3 + (5)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 = a and b = 5
⇒ (a)3 + (5)3 = (a + 5)((a)2 – (a)(5) + (5)2)
= (a + 5)(a2 – 5a + 25)
a3 + 123 = (a + 5)(a2 – 5a + 25)
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