Answer:
16y³ + 12x²y
Step-by-step explanation:
Using the identities
(a + b)³ = a³ + b³ + 3ab(a + b), with a = x and b = 2y
(x + 2y)³
= x³ + (2y)³ + 3x(2y)(x + 2y)
= x³ + 8y³ + 6xy(x + 2y)
= x³ + 8y³ +6x²y + 12xy² → (1)
And
(a - b)³ = a³ - b³ - 3ab(a - b), with a = x and b = 2y
(x - 2y)³
= x³ - (2y)³ - 3x(2y)(x - 2y)
= x³ - 8y³ - 6xy(x - 2y)
= x³ - 8y³ - 6x²y + 12xy² →(2)
(1) - (2)
= x³ + 8y³ + 6x²y + 12xy² - (x³ - 8y³ - 6x²y + 12xy²)
= x³ + 8y³ + 6x²y + 12xy² - x³ + 8y³ + 6x²y - 12xy² ← collect like terms
= 16y³ + 12x²y
