Find the Product -3x(x^2-7x-6)

$- 3 x (x^{2} - 7 x - 6)$

Step 1

Apply the distributive property.

$- 3 x \cdot x^{2} - 3 x (- 7 x) - 3 x \cdot - 6$

Step 2

Simplify.

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

Move $x^{2}$ .

$- 3 (x^{2} x) - 3 x (- 7 x) - 3 x \cdot - 6$

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

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

$- 3 (x^{2} x^{1}) - 3 x (- 7 x) - 3 x \cdot - 6$

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

$- 3 x^{2 + 1} - 3 x (- 7 x) - 3 x \cdot - 6$

Add $2$ and $1$ .

$- 3 x^{3} - 3 x (- 7 x) - 3 x \cdot - 6$

Rewrite using the commutative property of multiplication.

$- 3 x^{3} - 3 \cdot - 7 x \cdot x - 3 x \cdot - 6$

Multiply $- 6$ by $- 3$ .

$- 3 x^{3} - 3 \cdot - 7 x \cdot x + 18 x$

Step 3

Simplify each term.

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

Move $x$ .

$- 3 x^{3} - 3 \cdot - 7 (x \cdot x) + 18 x$

Multiply $x$ by $x$ .

$- 3 x^{3} - 3 \cdot - 7 x^{2} + 18 x$

Multiply $- 3$ by $- 7$ .

$- 3 x^{3} + 21 x^{2} + 18 x$