Worked-out examples for the expansion of cube of a binomial:Simplify the following by cubing:1. (x + 5y)3 + (x – 5y)3
Solution:
We know, (a + b)3 = a3 + 3a2b + 3ab2 + b3
and,
(a – b)3 = a3 – 3a2b + 3ab2 – b3
Here, a = x and b = 5y
Now using the formulas for cube of two binomials we get,
= x3 + 3.x2.5y + 3.x.(5y)2 + (5y)3 + x3 - 3.x2.5y + 3.x.(5y)2 - (5y)3
= x3 + 15x2y + 75xy2 + 125 y3 + x3 - 15x2y + 75xy2 - 125 y3
= 2x3 + 150xy2
Therefore, (x + 5y)3 + (x – 5y)3 = 2x3 + 150xy2
