Find the Product (x-3)(x^2-8x+2)

$(x - 3) (x^{2} - 8 x + 2)$

Step 1

Expand $(x - 3) (x^{2} - 8 x + 2)$ by multiplying each term in the first expression by each term in the second expression.

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

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 $1$ .

$x^{1} x^{2} + x (- 8 x) + x \cdot 2 - 3 x^{2} - 3 (- 8 x) - 3 \cdot 2$

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

$x^{1 + 2} + x (- 8 x) + x \cdot 2 - 3 x^{2} - 3 (- 8 x) - 3 \cdot 2$

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $2$ to the left of $x$ .

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

Multiply $- 8$ by $- 3$ .

$x^{3} - 8 x^{2} + 2 x - 3 x^{2} + 24 x - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$x^{3} - 8 x^{2} + 2 x - 3 x^{2} + 24 x - 6$

Simplify by adding terms.

Subtract $3 x^{2}$ from $- 8 x^{2}$ .

$x^{3} - 11 x^{2} + 2 x + 24 x - 6$

Add $2 x$ and $24 x$ .

$x^{3} - 11 x^{2} + 26 x - 6$