Simplify 3x^2(7x^2+2x-4)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 4$ by $3$ .

$3 \cdot 7 x^{2} x^{2} + 3 \cdot 2 x^{2} x - 12 x^{2}$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$3 \cdot 7 (x^{2} x^{2}) + 3 \cdot 2 x^{2} x - 12 x^{2}$

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

$3 \cdot 7 x^{2 + 2} + 3 \cdot 2 x^{2} x - 12 x^{2}$

Add $2$ and $2$ .

$3 \cdot 7 x^{4} + 3 \cdot 2 x^{2} x - 12 x^{2}$

Multiply $3$ by $7$ .

$21 x^{4} + 3 \cdot 2 x^{2} x - 12 x^{2}$

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

Move $x$ .

$21 x^{4} + 3 \cdot 2 (x \cdot x^{2}) - 12 x^{2}$

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

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

$21 x^{4} + 3 \cdot 2 (x^{1} x^{2}) - 12 x^{2}$

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

$21 x^{4} + 3 \cdot 2 x^{1 + 2} - 12 x^{2}$

Add $1$ and $2$ .

$21 x^{4} + 3 \cdot 2 x^{3} - 12 x^{2}$

Multiply $3$ by $2$ .

$21 x^{4} + 6 x^{3} - 12 x^{2}$