Simplify (x-3)(x-3)(x-3)

$(x - 3) (x - 3) (x - 3)$

Step 1

Multiply $x - 3$ by $x - 3$ .

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

Step 2

Multiply ${(x - 3)}^{2}$ by $x - 3$ by adding the exponents.

Multiply ${(x - 3)}^{2}$ by $x - 3$ .

Raise $x - 3$ to the power of $1$ .

${(x - 3)}^{2} {(x - 3)}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x - 3)}^{2 + 1}$

Add $2$ and $1$ .

${(x - 3)}^{3}$

Step 3

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot - 3 + 3 x {(- 3)}^{2} + {(- 3)}^{3}$

Step 4

Simplify each term.

Multiply $- 3$ by $3$ .

$x^{3} - 9 x^{2} + 3 x {(- 3)}^{2} + {(- 3)}^{3}$

Raise $- 3$ to the power of $2$ .

$x^{3} - 9 x^{2} + 3 x \cdot 9 + {(- 3)}^{3}$

Multiply $9$ by $3$ .

$x^{3} - 9 x^{2} + 27 x + {(- 3)}^{3}$

Raise $- 3$ to the power of $3$ .

$x^{3} - 9 x^{2} + 27 x - 27$