Question

What is the fifth term of (2x-2)^7

Answer 1

ANSWER


`T_(5) =4480 {x}^(3)`

Step-by-step explanation

We want to find the fifth term of the binomial expansion


`(2x - 2)^(7)`

When we compare to


`{(a + b)}^(n)`
we have n=7, a=2x and b=-2

For the 5th term,


`r + 1 = 5`

This means that,


`r = 4`

The fifth term can be found using the formula,


`T_(r+1) = ^nC_r {a}^(n - r) {b}^(r)`


`T_(5) = ^7C_4 {(2x)}^(7 - 4) {( - 2)}^(4)`

We substitute the values to obtain,


`T_(5) = ^7C_4 {(2x)}^(3) {( - 2)}^(4)`


`T_(5) = 35 * {8x}^(3) * 16`


`T_(5) =4480 {x}^(3)`