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

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $- 7$ by $- 4$ .

$- 4 \cdot 3 x^{2} x + 28 x^{2}$

Step 2

Simplify each term.

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

Move $x$ .

$- 4 \cdot 3 (x \cdot x^{2}) + 28 x^{2}$

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

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

$- 4 \cdot 3 (x^{1} x^{2}) + 28 x^{2}$

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

$- 4 \cdot 3 x^{1 + 2} + 28 x^{2}$

Add $1$ and $2$ .

$- 4 \cdot 3 x^{3} + 28 x^{2}$

Multiply $- 4$ by $3$ .

$- 12 x^{3} + 28 x^{2}$