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Problem 18 - Entrance Test
Expand (2x - y)(4x^2 + 2xy + y^2).
A. 8x^3 + y^3
B. 8x^3 - y^3
C. (2x - y)^3
D. 8x^3 - 4x^2y + 2xy^2 - y^3
Check Answer
Show Solution
Correct: B
This expression matches the identity (a - b)(a^2 + ab + b^2) = a^3 - b^3. Here, a = 2x and b = y. So, (2x - y)((2x)^2 + (2x)(y) + (y)^2) = (2x)^3 - (y)^3 = 8x^3 - y^3.