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The coefficient of x2 in the expansion of (1 + 2x)m  is 112. Find m.

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The coefficient of x2 in (1 + 2x)m = mC2 (22)

Given that the coefficient of x2  = 112

mC2  (4) = 112

∴ mC2  = 28

∴ m(m – 1) = 56

∴ m2  – m – 56 = 0

∴ (m – 8) (m + 7) = 0

As m cannot be negative.

∴ m = 8

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