Simplify -4x^2(6x-5x^2-5)

$- 4 x^{2} (6 x - 5 x^{2} - 5)$

Step 1

Apply the distributive property.

$- 4 x^{2} (6 x) - 4 x^{2} (- 5 x^{2}) - 4 x^{2} \cdot - 5$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 4 \cdot 6 x^{2} x - 4 x^{2} (- 5 x^{2}) - 4 x^{2} \cdot - 5$

Rewrite using the commutative property of multiplication.

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

Multiply $- 5$ by $- 4$ .

$- 4 \cdot 6 x^{2} x - 4 \cdot - 5 x^{2} x^{2} + 20 x^{2}$

Step 3

Simplify each term.

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

Move $x$ .

$- 4 \cdot 6 (x \cdot x^{2}) - 4 \cdot - 5 x^{2} x^{2} + 20 x^{2}$

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

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

$- 4 \cdot 6 (x^{1} x^{2}) - 4 \cdot - 5 x^{2} x^{2} + 20 x^{2}$

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

$- 4 \cdot 6 x^{1 + 2} - 4 \cdot - 5 x^{2} x^{2} + 20 x^{2}$

Add $1$ and $2$ .

$- 4 \cdot 6 x^{3} - 4 \cdot - 5 x^{2} x^{2} + 20 x^{2}$

Multiply $- 4$ by $6$ .

$- 24 x^{3} - 4 \cdot - 5 x^{2} x^{2} + 20 x^{2}$

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

Move $x^{2}$ .

$- 24 x^{3} - 4 \cdot - 5 (x^{2} x^{2}) + 20 x^{2}$

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

$- 24 x^{3} - 4 \cdot - 5 x^{2 + 2} + 20 x^{2}$

Add $2$ and $2$ .

$- 24 x^{3} - 4 \cdot - 5 x^{4} + 20 x^{2}$

Multiply $- 4$ by $- 5$ .

$- 24 x^{3} + 20 x^{4} + 20 x^{2}$

Step 4

Reorder $- 24 x^{3}$ and $20 x^{4}$ .

$20 x^{4} - 24 x^{3} + 20 x^{2}$