Find the Product -7x(3x^2-4x+9)

$- 7 x (3 x^{2} - 4 x + 9)$

Step 1

Apply the distributive property.

$- 7 x (3 x^{2}) - 7 x (- 4 x) - 7 x \cdot 9$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 7 \cdot 3 x \cdot x^{2} - 7 x (- 4 x) - 7 x \cdot 9$

Rewrite using the commutative property of multiplication.

$- 7 \cdot 3 x \cdot x^{2} - 7 \cdot - 4 x \cdot x - 7 x \cdot 9$

Multiply $9$ by $- 7$ .

$- 7 \cdot 3 x \cdot x^{2} - 7 \cdot - 4 x \cdot x - 63 x$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$- 7 \cdot 3 (x^{2} x) - 7 \cdot - 4 x \cdot x - 63 x$

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

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

$- 7 \cdot 3 (x^{2} x^{1}) - 7 \cdot - 4 x \cdot x - 63 x$

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

$- 7 \cdot 3 x^{2 + 1} - 7 \cdot - 4 x \cdot x - 63 x$

Add $2$ and $1$ .

$- 7 \cdot 3 x^{3} - 7 \cdot - 4 x \cdot x - 63 x$

Multiply $- 7$ by $3$ .

$- 21 x^{3} - 7 \cdot - 4 x \cdot x - 63 x$

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

Move $x$ .

$- 21 x^{3} - 7 \cdot - 4 (x \cdot x) - 63 x$

Multiply $x$ by $x$ .

$- 21 x^{3} - 7 \cdot - 4 x^{2} - 63 x$

Multiply $- 7$ by $- 4$ .

$- 21 x^{3} + 28 x^{2} - 63 x$