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Problem 9 - Entrance Test
Expand (m - 2n)^3.
A. m^3 - 8n^3
B. m^3 - 6m^2n + 12mn^2 - 8n^3
C. m^3 + 6m^2n + 12mn^2 + 8n^3
D. m^3 - 4m^2n + 8mn^2 - 8n^3
Check Answer
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Correct: B
Using the identity (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3, here a = m and b = 2n. (m - 2n)^3 = (m)^3 - 3(m)^2(2n) + 3(m)(2n)^2 - (2n)^3 = m^3 - 3(m^2)(2n) + 3(m)(4n^2) - 8n^3 = m^3 - 6m^2n + 12mn^2 - 8n^3.