ANSWER
[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]
EXPLANATION
We want to expand:
[tex] {(x - 3)}^3[/tex]
Using the identity;
[tex] {(x - y)}^{3} = {x}^{3} - 3 {x}^{2}y + 3x {y}^{2} - {y}^{3} [/tex]
We substitute y=3 into the above identity to obtain:
[tex] {(x - 3)}^{3} = {x}^{3} - 3 {x}^{2}(3) + 3x( {3}^{2} ) - {(3)}^{3} [/tex]
Let us simplify to get:
[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]
