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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $- 2$ .

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

Step 3

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $- 2$ by $3$ .

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