Simplify 2p^3(p^2-4p-7)+5p(p^4-p^2)

$2 p^{3} (p^{2} - 4 p - 7) + 5 p (p^{4} - p^{2})$

Step 1

Simplify each term.

Apply the distributive property.

$2 p^{3} p^{2} + 2 p^{3} (- 4 p) + 2 p^{3} \cdot - 7 + 5 p (p^{4} - p^{2})$

Simplify.

Multiply $p^{3}$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$2 (p^{2} p^{3}) + 2 p^{3} (- 4 p) + 2 p^{3} \cdot - 7 + 5 p (p^{4} - p^{2})$

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

$2 p^{2 + 3} + 2 p^{3} (- 4 p) + 2 p^{3} \cdot - 7 + 5 p (p^{4} - p^{2})$

Add $2$ and $3$ .

$2 p^{5} + 2 p^{3} (- 4 p) + 2 p^{3} \cdot - 7 + 5 p (p^{4} - p^{2})$

Rewrite using the commutative property of multiplication.

$2 p^{5} + 2 \cdot - 4 p^{3} p + 2 p^{3} \cdot - 7 + 5 p (p^{4} - p^{2})$

Multiply $- 7$ by $2$ .

$2 p^{5} + 2 \cdot - 4 p^{3} p - 14 p^{3} + 5 p (p^{4} - p^{2})$

Simplify each term.

Multiply $p^{3}$ by $p$ by adding the exponents.

Move $p$ .

$2 p^{5} + 2 \cdot - 4 (p \cdot p^{3}) - 14 p^{3} + 5 p (p^{4} - p^{2})$

Multiply $p$ by $p^{3}$ .

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

$2 p^{5} + 2 \cdot - 4 (p^{1} p^{3}) - 14 p^{3} + 5 p (p^{4} - p^{2})$

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

$2 p^{5} + 2 \cdot - 4 p^{1 + 3} - 14 p^{3} + 5 p (p^{4} - p^{2})$

Add $1$ and $3$ .

$2 p^{5} + 2 \cdot - 4 p^{4} - 14 p^{3} + 5 p (p^{4} - p^{2})$

Multiply $2$ by $- 4$ .

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p (p^{4} - p^{2})$

Apply the distributive property.

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p \cdot p^{4} + 5 p (- p^{2})$

Multiply $p$ by $p^{4}$ by adding the exponents.

Move $p^{4}$ .

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 (p^{4} p) + 5 p (- p^{2})$

Multiply $p^{4}$ by $p$ .

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

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 (p^{4} p^{1}) + 5 p (- p^{2})$

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

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{4 + 1} + 5 p (- p^{2})$

Add $4$ and $1$ .

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} + 5 p (- p^{2})$

Rewrite using the commutative property of multiplication.

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} + 5 \cdot - 1 p \cdot p^{2}$

Simplify each term.

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

Move $p^{2}$ .

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} + 5 \cdot - 1 (p^{2} p)$

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

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

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} + 5 \cdot - 1 (p^{2} p^{1})$

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

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} + 5 \cdot - 1 p^{2 + 1}$

Add $2$ and $1$ .

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} + 5 \cdot - 1 p^{3}$

Multiply $5$ by $- 1$ .

$2 p^{5} - 8 p^{4} - 14 p^{3} + 5 p^{5} - 5 p^{3}$

Step 2

Simplify by adding terms.

Add $2 p^{5}$ and $5 p^{5}$ .

$7 p^{5} - 8 p^{4} - 14 p^{3} - 5 p^{3}$

Subtract $5 p^{3}$ from $- 14 p^{3}$ .

$7 p^{5} - 8 p^{4} - 19 p^{3}$

Simplify 2p^3(p^2-4p-7)+5p(p^4-p^2)

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