Question

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

• A. 24
• B. 18
• C. 12
• D. 16

Answer 1

Answer:

A. 24

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.