Determine the coefficient of x^8 in the expansion of (2 − 3x^2)^7 .

Question

we want to find the coefficient of x^8 in the expansion of (2-3x^2)^7

Answer 1

x⁸ comes from -3x², which needs to be raised to the fourth power: (-3x²)⁴=81x⁸.

Take (a+b)⁷, where a and b are any quantities. The expansion is:

a⁷+7a⁶b+21a⁵b²+35a⁴b³+35a³b⁴+...

35a³b⁴ is the term we need to compute when a=2 and b=-3x².

a³=8, b⁴=81x⁸, as we saw earlier.

So the coefficient is 35×8×81=22680.