Factorize and simplify

Question

(3x+y)³+(3x-y)³

Answer 1

To factorize and simplify the given expression:
(3x + y)³ + (3x - y)³

First, let's expand each cubed term using the formula (a ± b)³ = a³ ± 3a²b ± 3ab² ± b³:

(3x + y)³ = (3x)³ + 3(3x)²(y) + 3(3x)(y)² + (y)³
= 27x³ + 27x²y + 9xy² + y³

(3x - y)³ = (3x)³ - 3(3x)²(y) + 3(3x)(y)² - (y)³
= 27x³ - 27x²y + 9xy² - y³

Now, we can add the two expanded expressions together:

(27x³ + 27x²y + 9xy² + y³) + (27x³ - 27x²y + 9xy² - y³)
= 2(27x³) + 2(9xy²)
= 54x³ + 18xy²

Therefore, the factorized and simplified form of the expression (3x + y)³ + (3x - y)³ is 54x³ + 18xy².