Simplify -4x^2(5x^4-3x^2+x-2)

$- 4 x^{2} (5 x^{4} - 3 x^{2} + x - 2)$

Apply the distributive property.

$- 4 x^{2} (5 x^{4}) - 4 x^{2} (- 3 x^{2}) - 4 x^{2} x - 4 x^{2} \cdot - 2$

Simplify.

Rewrite using the commutative property of multiplication.

$- 4 \cdot 5 x^{2} x^{4} - 4 x^{2} (- 3 x^{2}) - 4 x^{2} x - 4 x^{2} \cdot - 2$

Rewrite using the commutative property of multiplication.

$- 4 \cdot 5 x^{2} x^{4} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{2} x - 4 x^{2} \cdot - 2$

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

Move $x$ .

$- 4 \cdot 5 x^{2} x^{4} - 4 \cdot - 3 x^{2} x^{2} - 4 (x \cdot x^{2}) - 4 x^{2} \cdot - 2$

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

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

$- 4 \cdot 5 x^{2} x^{4} - 4 \cdot - 3 x^{2} x^{2} - 4 (x^{1} x^{2}) - 4 x^{2} \cdot - 2$

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

$- 4 \cdot 5 x^{2} x^{4} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{1 + 2} - 4 x^{2} \cdot - 2$

Add $1$ and $2$ .

$- 4 \cdot 5 x^{2} x^{4} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{3} - 4 x^{2} \cdot - 2$

Multiply $- 2$ by $- 4$ .

$- 4 \cdot 5 x^{2} x^{4} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{3} + 8 x^{2}$

Simplify each term.

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$- 4 \cdot 5 (x^{4} x^{2}) - 4 \cdot - 3 x^{2} x^{2} - 4 x^{3} + 8 x^{2}$

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

$- 4 \cdot 5 x^{4 + 2} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{3} + 8 x^{2}$

Add $4$ and $2$ .

$- 4 \cdot 5 x^{6} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{3} + 8 x^{2}$

Multiply $- 4$ by $5$ .

$- 20 x^{6} - 4 \cdot - 3 x^{2} x^{2} - 4 x^{3} + 8 x^{2}$

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

Move $x^{2}$ .

$- 20 x^{6} - 4 \cdot - 3 (x^{2} x^{2}) - 4 x^{3} + 8 x^{2}$

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

$- 20 x^{6} - 4 \cdot - 3 x^{2 + 2} - 4 x^{3} + 8 x^{2}$

Add $2$ and $2$ .

$- 20 x^{6} - 4 \cdot - 3 x^{4} - 4 x^{3} + 8 x^{2}$

Multiply $- 4$ by $- 3$ .

$- 20 x^{6} + 12 x^{4} - 4 x^{3} + 8 x^{2}$