Find the coefficient of x^4 in the expansion of (4x-1) ^5

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 1

1 5 10 10 5 1

Example: write out (x + y) ^3:

Use the 4th row of Pascal's Triangle: 1 (x^3) + 3 (x^2) + 3 (x^1) + 1. Note how

the 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.