Find the Product -x(2x^3-x^2+6x-8)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 1 \cdot 2 x \cdot x^{3} - x (- x^{2}) - x (6 x) - x \cdot - 8$

Rewrite using the commutative property of multiplication.

$- 1 \cdot 2 x \cdot x^{3} - 1 \cdot - 1 x \cdot x^{2} - x (6 x) - x \cdot - 8$

Rewrite using the commutative property of multiplication.

$- 1 \cdot 2 x \cdot x^{3} - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x - x \cdot - 8$

Multiply $- 8$ by $- 1$ .

$- 1 \cdot 2 x \cdot x^{3} - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x + 8 x$

Step 3

Simplify each term.

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 1 \cdot 2 (x^{3} x) - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x + 8 x$

Multiply $x^{3}$ by $x$ .

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

$- 1 \cdot 2 (x^{3} x^{1}) - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x + 8 x$

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

$- 1 \cdot 2 x^{3 + 1} - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x + 8 x$

Add $3$ and $1$ .

$- 1 \cdot 2 x^{4} - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x + 8 x$

Multiply $- 1$ by $2$ .

$- 2 x^{4} - 1 \cdot - 1 x \cdot x^{2} - 1 \cdot 6 x \cdot x + 8 x$

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

Move $x^{2}$ .

$- 2 x^{4} - 1 \cdot - 1 (x^{2} x) - 1 \cdot 6 x \cdot x + 8 x$

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

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

$- 2 x^{4} - 1 \cdot - 1 (x^{2} x^{1}) - 1 \cdot 6 x \cdot x + 8 x$

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

$- 2 x^{4} - 1 \cdot - 1 x^{2 + 1} - 1 \cdot 6 x \cdot x + 8 x$

Add $2$ and $1$ .

$- 2 x^{4} - 1 \cdot - 1 x^{3} - 1 \cdot 6 x \cdot x + 8 x$

Multiply $- 1$ by $- 1$ .

$- 2 x^{4} + 1 x^{3} - 1 \cdot 6 x \cdot x + 8 x$

Multiply $x^{3}$ by $1$ .

$- 2 x^{4} + x^{3} - 1 \cdot 6 x \cdot x + 8 x$

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

Move $x$ .

$- 2 x^{4} + x^{3} - 1 \cdot 6 (x \cdot x) + 8 x$

Multiply $x$ by $x$ .

$- 2 x^{4} + x^{3} - 1 \cdot 6 x^{2} + 8 x$

Multiply $- 1$ by $6$ .

$- 2 x^{4} + x^{3} - 6 x^{2} + 8 x$

Find the Product -x(2x^3-x^2+6x-8)

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