Question

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

Answer 1

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