Algebra Examples

$9 p^{12} q^{7} - 2 p^{5} q^{6} \cdot 4 p^{7} q$

Step 1

Simplify each term.

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Step 1.1

Multiply $p^{5}$ by $p^{7}$ by adding the exponents.

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Step 1.1.1

Move $p^{7}$ .

$9 p^{12} q^{7} - 2 (p^{7} p^{5}) q^{6} \cdot (4 q)$

Step 1.1.2

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

$9 p^{12} q^{7} - 2 p^{7 + 5} q^{6} \cdot (4 q)$

Step 1.1.3

Add $7$ and $5$ .

$9 p^{12} q^{7} - 2 p^{12} q^{6} \cdot (4 q)$

Step 1.2

Multiply $q^{6}$ by $q$ by adding the exponents.

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Step 1.2.1

Move $q$ .

$9 p^{12} q^{7} - 2 p^{12} (q \cdot q^{6}) \cdot 4$

Step 1.2.2

Multiply $q$ by $q^{6}$ .

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Step 1.2.2.1

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

$9 p^{12} q^{7} - 2 p^{12} (q^{1} q^{6}) \cdot 4$

Step 1.2.2.2

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

$9 p^{12} q^{7} - 2 p^{12} q^{1 + 6} \cdot 4$

Step 1.2.3

Add $1$ and $6$ .

$9 p^{12} q^{7} - 2 p^{12} q^{7} \cdot 4$

Step 1.3

Multiply $4$ by $- 2$ .

$9 p^{12} q^{7} - 8 p^{12} q^{7}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 p^{12} q^{7}$ from $9 p^{12} q^{7}$ .

$1 p^{12} q^{7}$

Step 2.2

Multiply $p^{12}$ by $1$ .

$p^{12} q^{7}$