Simplify (x-6)(x^2-8x+9)

$(x - 6) (x^{2} - 8 x + 9)$

Step 1

Expand $(x - 6) (x^{2} - 8 x + 9)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (- 8 x) + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Step 2

Simplify terms.

Simplify each term.

Multiply $x$ by $x^{2}$ by adding the exponents.

Multiply $x$ by $x^{2}$ .

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

$x^{1} x^{2} + x (- 8 x) + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

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

$x^{1 + 2} + x (- 8 x) + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Add $1$ and $2$ .

$x^{3} + x (- 8 x) + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Rewrite using the commutative property of multiplication.

$x^{3} - 8 x \cdot x + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{3} - 8 (x \cdot x) + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Multiply $x$ by $x$ .

$x^{3} - 8 x^{2} + x \cdot 9 - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Move $9$ to the left of $x$ .

$x^{3} - 8 x^{2} + 9 \cdot x - 6 x^{2} - 6 (- 8 x) - 6 \cdot 9$

Multiply $- 8$ by $- 6$ .

$x^{3} - 8 x^{2} + 9 x - 6 x^{2} + 48 x - 6 \cdot 9$

Multiply $- 6$ by $9$ .

$x^{3} - 8 x^{2} + 9 x - 6 x^{2} + 48 x - 54$

Simplify by adding terms.

Subtract $6 x^{2}$ from $- 8 x^{2}$ .

$x^{3} - 14 x^{2} + 9 x + 48 x - 54$

Add $9 x$ and $48 x$ .

$x^{3} - 14 x^{2} + 57 x - 54$