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.

the answer is 375 miles

step-by-step explanation:

111

step-by-step explanation: