ANSWER
[tex]{(2x - 3)}^{3} = {8x}^{3} - 36 {x}^{2} + 54x - 27[/tex]
EXPLANATION
Using the binomial theorem of Pascal's triangle, the coefficient of the third exponent binomial is :
1,3,3,1
The expansion for
[tex] {(a - b)}^{3} = {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} [/tex]
To find the expansion for:
[tex] {(2x - 3)}^{3} [/tex]
We put a=2x and b=3
This implies that,
[tex]{(2x - 3)}^{3} = {(2x)}^{3} - 3 {(2x)}^{2} ( 3) + 3(2x) {(3)}^{2} - {3}^{3} [/tex]
This simplifies to:
[tex]{(2x - 3)}^{3} = {8x}^{3} - 36 {x}^{2} + 54x - 27[/tex]
