Question

I quickly need the answer. simplify (x + 2y)³ - (x - 2y)³​

Answer 1

16y³ + 12x²y

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

Answer 2

Good morning,

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Answer:

(x + 2y)³ - (x - 2y)³​ = 16y³ + 12x²y.

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Explanation:

Look at the photo below for the details.

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