Find the Product -6x^2(x^3+7x^2-4x+3)

$- 6 x^{2} (x^{3} + 7 x^{2} - 4 x + 3)$

Step 1

Apply the distributive property.

$- 6 x^{2} x^{3} - 6 x^{2} (7 x^{2}) - 6 x^{2} (- 4 x) - 6 x^{2} \cdot 3$

Step 2

Simplify.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 6 (x^{3} x^{2}) - 6 x^{2} (7 x^{2}) - 6 x^{2} (- 4 x) - 6 x^{2} \cdot 3$

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

$- 6 x^{3 + 2} - 6 x^{2} (7 x^{2}) - 6 x^{2} (- 4 x) - 6 x^{2} \cdot 3$

Add $3$ and $2$ .

$- 6 x^{5} - 6 x^{2} (7 x^{2}) - 6 x^{2} (- 4 x) - 6 x^{2} \cdot 3$

Rewrite using the commutative property of multiplication.

$- 6 x^{5} - 6 \cdot 7 x^{2} x^{2} - 6 x^{2} (- 4 x) - 6 x^{2} \cdot 3$

Rewrite using the commutative property of multiplication.

$- 6 x^{5} - 6 \cdot 7 x^{2} x^{2} - 6 \cdot - 4 x^{2} x - 6 x^{2} \cdot 3$

Multiply $3$ by $- 6$ .

$- 6 x^{5} - 6 \cdot 7 x^{2} x^{2} - 6 \cdot - 4 x^{2} x - 18 x^{2}$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$- 6 x^{5} - 6 \cdot 7 (x^{2} x^{2}) - 6 \cdot - 4 x^{2} x - 18 x^{2}$

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

$- 6 x^{5} - 6 \cdot 7 x^{2 + 2} - 6 \cdot - 4 x^{2} x - 18 x^{2}$

Add $2$ and $2$ .

$- 6 x^{5} - 6 \cdot 7 x^{4} - 6 \cdot - 4 x^{2} x - 18 x^{2}$

Multiply $- 6$ by $7$ .

$- 6 x^{5} - 42 x^{4} - 6 \cdot - 4 x^{2} x - 18 x^{2}$

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

Move $x$ .

$- 6 x^{5} - 42 x^{4} - 6 \cdot - 4 (x \cdot x^{2}) - 18 x^{2}$

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

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

$- 6 x^{5} - 42 x^{4} - 6 \cdot - 4 (x^{1} x^{2}) - 18 x^{2}$

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

$- 6 x^{5} - 42 x^{4} - 6 \cdot - 4 x^{1 + 2} - 18 x^{2}$

Add $1$ and $2$ .

$- 6 x^{5} - 42 x^{4} - 6 \cdot - 4 x^{3} - 18 x^{2}$

Multiply $- 6$ by $- 4$ .

$- 6 x^{5} - 42 x^{4} + 24 x^{3} - 18 x^{2}$