Simplify x(-7x^2-8x)

$x (- 7 x^{2} - 8 x)$

Simplify by multiplying through.

Apply the distributive property.

$x (- 7 x^{2}) + x (- 8 x)$

Reorder.

Rewrite using the commutative property of multiplication.

$- 7 x \cdot x^{2} + x (- 8 x)$

Rewrite using the commutative property of multiplication.

$- 7 x \cdot x^{2} - 8 x \cdot x$

Simplify each term.

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

Move $x^{2}$ .

$- 7 (x^{2} x) - 8 x \cdot x$

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

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

$- 7 (x^{2} x^{1}) - 8 x \cdot x$

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

$- 7 x^{2 + 1} - 8 x \cdot x$

Add $2$ and $1$ .

$- 7 x^{3} - 8 x \cdot x$

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

Move $x$ .

$- 7 x^{3} - 8 (x \cdot x)$

Multiply $x$ by $x$ .

$- 7 x^{3} - 8 x^{2}$