If x + y = 4, then the value of (x3 + y3 + 12xy) is

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If x + y = 4, then the value of (x³ + y³ + 12xy) is

A64

B16

D256

Answer:

Given:

x + y = 4

Formula Used:

(x + y)³ = x³ + y³ + 3xy (x + y)

Calculation:

Here, x + y = 4

So, x³ + y³ + 12xy = x³ + y³ + 3xy $\times$ 4

⇒ x³ + y³ + 12xy = x³ + y³ + 3xy (x + y) = (x + y)³

⇒ x³ + y³ + 12xy = 4³

⇒ x3 + y3 + 12xy = 64

∴ The value of x3 + y3 + 12xy is 64.

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