Simplify 2p(-4p^2+5p)-5(2p^2+20)

$2 p (- 4 p^{2} + 5 p) - 5 (2 p^{2} + 20)$

Step 1

Simplify each term.

Apply the distributive property.

$2 p (- 4 p^{2}) + 2 p (5 p) - 5 (2 p^{2} + 20)$

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Simplify each term.

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

Move $p^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $- 4$ .

$- 8 p^{3} + 2 \cdot 5 p \cdot p - 5 (2 p^{2} + 20)$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$- 8 p^{3} + 2 \cdot 5 (p \cdot p) - 5 (2 p^{2} + 20)$

Multiply $p$ by $p$ .

$- 8 p^{3} + 2 \cdot 5 p^{2} - 5 (2 p^{2} + 20)$

Multiply $2$ by $5$ .

$- 8 p^{3} + 10 p^{2} - 5 (2 p^{2} + 20)$

Apply the distributive property.

$- 8 p^{3} + 10 p^{2} - 5 (2 p^{2}) - 5 \cdot 20$

Multiply $2$ by $- 5$ .

$- 8 p^{3} + 10 p^{2} - 10 p^{2} - 5 \cdot 20$

Multiply $- 5$ by $20$ .

$- 8 p^{3} + 10 p^{2} - 10 p^{2} - 100$

Step 2

Combine the opposite terms in $- 8 p^{3} + 10 p^{2} - 10 p^{2} - 100$ .

Subtract $10 p^{2}$ from $10 p^{2}$ .

$- 8 p^{3} + 0 - 100$

Add $- 8 p^{3}$ and $0$ .

$- 8 p^{3} - 100$