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In the expansion of (2x+y)3−(2x−y)3(2x + y )^3-(2x - y)^3, the coefficient of x2yx^2y is:

A24

B18

C12

D16

Answer:

A. 24

Read Explanation:

Solution:

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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