Simplify -4x^2(6x^2+x)

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

Step 1

Apply the distributive property.

$- 4 x^{2} (6 x^{2}) - 4 x^{2} x$

Step 2

Rewrite using the commutative property of multiplication.

$- 4 \cdot 6 x^{2} x^{2} - 4 x^{2} x$

Step 3

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 4

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$- 4 \cdot 6 x^{4} - 4 x^{3}$

Multiply $- 4$ by $6$ .

$- 24 x^{4} - 4 x^{3}$