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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Move $- 3$ to the left of $x^{2}$ .

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

Step 3

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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