Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $p^{2}$ .

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

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

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

Step 1.4.1.2.2

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

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

Step 1.4.1.3

Add $2$ and $1$ .

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

Step 1.4.2

Multiply $2$ by $- 4$ .

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

Step 1.4.3

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

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Step 1.4.3.1

Move $p$ .

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

Step 1.4.3.2

Multiply $p$ by $p$ .

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

Step 1.4.4

Multiply $2$ by $5$ .

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Multiply $2$ by $- 5$ .

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

Step 1.7

Multiply $- 5$ by $20$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

$- 8 p^{3} - 100$