Algebra Examples

$9 p^{7} q^{9} + 10 p^{4} q^{8} \cdot (- 2 p^{3} q)$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Move $p^{3}$ .

$9 p^{7} q^{9} + 10 (p^{3} p^{4}) q^{8} \cdot (- 2 q)$

Step 1.1.2

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

$9 p^{7} q^{9} + 10 p^{3 + 4} q^{8} \cdot (- 2 q)$

Step 1.1.3

Add $3$ and $4$ .

$9 p^{7} q^{9} + 10 p^{7} q^{8} \cdot (- 2 q)$

Step 1.2

Multiply $q^{8}$ by $q$ by adding the exponents.

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Step 1.2.1

Move $q$ .

$9 p^{7} q^{9} + 10 p^{7} (q \cdot q^{8}) \cdot - 2$

Step 1.2.2

Multiply $q$ by $q^{8}$ .

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Step 1.2.2.1

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

$9 p^{7} q^{9} + 10 p^{7} (q^{1} q^{8}) \cdot - 2$

Step 1.2.2.2

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

$9 p^{7} q^{9} + 10 p^{7} q^{1 + 8} \cdot - 2$

Step 1.2.3

Add $1$ and $8$ .

$9 p^{7} q^{9} + 10 p^{7} q^{9} \cdot - 2$

Step 1.3

Multiply $- 2$ by $10$ .

$9 p^{7} q^{9} - 20 p^{7} q^{9}$

Step 2

Subtract $20 p^{7} q^{9}$ from $9 p^{7} q^{9}$ .

$- 11 p^{7} q^{9}$