In the expansion of $(2x + y )^3-(2x - y)^3$, the coefficient of $x^2y$ is:

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In the expansion of $(2x + y )^3-(2x - y)^3$ , the coefficient of $x^2y$ is:

A24

B18

C12

D16

Answer:

Formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

Calculation:

(2x + y)³ = 8x³ + 12x²y + 6xy² + y³

(2x - y) = 8x³ - 12x²y + 6xy² - y³

( 2x + y )³- ( 2x - y)³ = 8x³ + 12x²y + 6xy² + y³- 8x³ + 12x²y - 6xy² + y³

( 2x + y )³- ( 2x - y)³ = 24x²y + 2y³

∴ The coefficient of x²y is 24.

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