Simplify -3p^4r^3(2p^2r^4-6p^6r^3-5)

$- 3 p^{4} r^{3} (2 p^{2} r^{4} - 6 p^{6} r^{3} - 5)$

Step 1

Apply the distributive property.

$- 3 p^{4} r^{3} (2 p^{2} r^{4}) - 3 p^{4} r^{3} (- 6 p^{6} r^{3}) - 3 p^{4} r^{3} \cdot - 5$

Step 2

Simplify.

Multiply $p^{4}$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$- 3 (p^{2} p^{4}) r^{3} (2 r^{4}) - 3 p^{4} r^{3} (- 6 p^{6} r^{3}) - 3 p^{4} r^{3} \cdot - 5$

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

$- 3 p^{2 + 4} r^{3} (2 r^{4}) - 3 p^{4} r^{3} (- 6 p^{6} r^{3}) - 3 p^{4} r^{3} \cdot - 5$

Add $2$ and $4$ .

$- 3 p^{6} r^{3} (2 r^{4}) - 3 p^{4} r^{3} (- 6 p^{6} r^{3}) - 3 p^{4} r^{3} \cdot - 5$

Multiply $p^{4}$ by $p^{6}$ by adding the exponents.

Move $p^{6}$ .

$- 3 p^{6} r^{3} (2 r^{4}) - 3 (p^{6} p^{4}) r^{3} (- 6 r^{3}) - 3 p^{4} r^{3} \cdot - 5$

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

$- 3 p^{6} r^{3} (2 r^{4}) - 3 p^{6 + 4} r^{3} (- 6 r^{3}) - 3 p^{4} r^{3} \cdot - 5$

Add $6$ and $4$ .

$- 3 p^{6} r^{3} (2 r^{4}) - 3 p^{10} r^{3} (- 6 r^{3}) - 3 p^{4} r^{3} \cdot - 5$

Multiply $- 5$ by $- 3$ .

$- 3 p^{6} r^{3} (2 r^{4}) - 3 p^{10} r^{3} (- 6 r^{3}) + 15 p^{4} r^{3}$

Step 3

Simplify each term.

Multiply $r^{3}$ by $r^{4}$ by adding the exponents.

Move $r^{4}$ .

$- 3 p^{6} (r^{4} r^{3}) \cdot 2 - 3 p^{10} r^{3} (- 6 r^{3}) + 15 p^{4} r^{3}$

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

$- 3 p^{6} r^{4 + 3} \cdot 2 - 3 p^{10} r^{3} (- 6 r^{3}) + 15 p^{4} r^{3}$

Add $4$ and $3$ .

$- 3 p^{6} r^{7} \cdot 2 - 3 p^{10} r^{3} (- 6 r^{3}) + 15 p^{4} r^{3}$

Multiply $2$ by $- 3$ .

$- 6 p^{6} r^{7} - 3 p^{10} r^{3} (- 6 r^{3}) + 15 p^{4} r^{3}$

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

Move $r^{3}$ .

$- 6 p^{6} r^{7} - 3 p^{10} (r^{3} r^{3}) \cdot - 6 + 15 p^{4} r^{3}$

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

$- 6 p^{6} r^{7} - 3 p^{10} r^{3 + 3} \cdot - 6 + 15 p^{4} r^{3}$

Add $3$ and $3$ .

$- 6 p^{6} r^{7} - 3 p^{10} r^{6} \cdot - 6 + 15 p^{4} r^{3}$

Multiply $- 6$ by $- 3$ .

$- 6 p^{6} r^{7} + 18 p^{10} r^{6} + 15 p^{4} r^{3}$