MATH SOLVE

2 months ago

Q:
# find the coefficient of x^4 in the expansion of (4x-1)^5

Accepted Solution

A:

Answer:The coeff. of x^4 in this expansion is -1280.Step-by-step explanation:Start by writing down a Pascal's Triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 11 5 10 10 5 1Example: write out (x + y)^3:Use the 4th row of Pascal's Triangle: 1(x^3) + 3(x^2) + 3(x^1) + 1. Note howthe powers of x decrease from 3 through 2, 1 and 0.Now let's apply this to the problem at hand. Use the coefficients in the 6th row of the Triangle, above:1[4x]^5 + 5[4x]^4·(-1) + ....The first term is 1[4x]^5, or [4x]^5, or 4^5·x^5, or 1024·x^5.The second term is 5[4x]^4·(-1), or 5·4^4·(-1), or 5[256](-1) = -1280.Thus, the coeff. of x^4 in this expansion is -1280.