Find the Product 2pr^2(2pr+5p^2r-15p)

$2 p r^{2} (2 p r + 5 p^{2} r - 15 p)$

Step 1

Apply the distributive property.

$2 p r^{2} (2 p r) + 2 p r^{2} (5 p^{2} r) + 2 p r^{2} (- 15 p)$

Step 2

Simplify.

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

Move $p$ .

$2 (p \cdot p) r^{2} (2 r) + 2 p r^{2} (5 p^{2} r) + 2 p r^{2} (- 15 p)$

Multiply $p$ by $p$ .

$2 p^{2} r^{2} (2 r) + 2 p r^{2} (5 p^{2} r) + 2 p r^{2} (- 15 p)$

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

Move $p^{2}$ .

$2 p^{2} r^{2} (2 r) + 2 (p^{2} p) r^{2} (5 r) + 2 p r^{2} (- 15 p)$

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

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

$2 p^{2} r^{2} (2 r) + 2 (p^{2} p^{1}) r^{2} (5 r) + 2 p r^{2} (- 15 p)$

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

$2 p^{2} r^{2} (2 r) + 2 p^{2 + 1} r^{2} (5 r) + 2 p r^{2} (- 15 p)$

Add $2$ and $1$ .

$2 p^{2} r^{2} (2 r) + 2 p^{3} r^{2} (5 r) + 2 p r^{2} (- 15 p)$

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

Move $p$ .

$2 p^{2} r^{2} (2 r) + 2 p^{3} r^{2} (5 r) + 2 (p \cdot p) r^{2} \cdot - 15$

Multiply $p$ by $p$ .

$2 p^{2} r^{2} (2 r) + 2 p^{3} r^{2} (5 r) + 2 p^{2} r^{2} \cdot - 15$

Step 3

Simplify each term.

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

Move $r$ .

$2 p^{2} (r \cdot r^{2}) \cdot 2 + 2 p^{3} r^{2} (5 r) + 2 p^{2} r^{2} \cdot - 15$

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

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

$2 p^{2} (r^{1} r^{2}) \cdot 2 + 2 p^{3} r^{2} (5 r) + 2 p^{2} r^{2} \cdot - 15$

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

$2 p^{2} r^{1 + 2} \cdot 2 + 2 p^{3} r^{2} (5 r) + 2 p^{2} r^{2} \cdot - 15$

Add $1$ and $2$ .

$2 p^{2} r^{3} \cdot 2 + 2 p^{3} r^{2} (5 r) + 2 p^{2} r^{2} \cdot - 15$

Multiply $2$ by $2$ .

$4 p^{2} r^{3} + 2 p^{3} r^{2} (5 r) + 2 p^{2} r^{2} \cdot - 15$

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

Move $r$ .

$4 p^{2} r^{3} + 2 p^{3} (r \cdot r^{2}) \cdot 5 + 2 p^{2} r^{2} \cdot - 15$

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

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

$4 p^{2} r^{3} + 2 p^{3} (r^{1} r^{2}) \cdot 5 + 2 p^{2} r^{2} \cdot - 15$

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

$4 p^{2} r^{3} + 2 p^{3} r^{1 + 2} \cdot 5 + 2 p^{2} r^{2} \cdot - 15$

Add $1$ and $2$ .

$4 p^{2} r^{3} + 2 p^{3} r^{3} \cdot 5 + 2 p^{2} r^{2} \cdot - 15$

Multiply $5$ by $2$ .

$4 p^{2} r^{3} + 10 p^{3} r^{3} + 2 p^{2} r^{2} \cdot - 15$

Multiply $- 15$ by $2$ .

$4 p^{2} r^{3} + 10 p^{3} r^{3} - 30 p^{2} r^{2}$

Find the Product 2pr^2(2pr+5p^2r-15p)

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