Question

Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.

_ (2x-3)^3

HELP ASAP

Answer 1

`{(2x - 3)}^(3) = {8x}^(3) - 36 {x}^(2) + 54x - 27`

Step-by-step explanation

Using the binomial theorem of Pascal's triangle, the coefficient of the third exponent binomial is :

1,3,3,1

The expansion for

`{(a - b)}^(3) = {a}^(3) - 3 {a}^(2) b + 3a {b}^(2) - {b}^(3)`

To find the expansion for:

`{(2x - 3)}^(3)`

We put a=2x and b=3

This implies that,

`{(2x - 3)}^(3) = {(2x)}^(3) - 3 {(2x)}^(2) ( 3) + 3(2x) {(3)}^(2) - {3}^(3)`

This simplifies to:

`{(2x - 3)}^(3) = {8x}^(3) - 36 {x}^(2) + 54x - 27`