Algebra Examples

$(10 a^{4} b^{6}) (3 a^{5} b^{2}) - 7 a^{9} b^{8}$

Step 1

Simplify each term.

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Step 1.1

Multiply $a^{4}$ by $a^{5}$ by adding the exponents.

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Step 1.1.1

Move $a^{5}$ .

$10 (a^{5} a^{4}) b^{6} (3 b^{2}) - 7 a^{9} b^{8}$

Step 1.1.2

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

$10 a^{5 + 4} b^{6} (3 b^{2}) - 7 a^{9} b^{8}$

Step 1.1.3

Add $5$ and $4$ .

$10 a^{9} b^{6} (3 b^{2}) - 7 a^{9} b^{8}$

Step 1.2

Multiply $b^{6}$ by $b^{2}$ by adding the exponents.

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Step 1.2.1

Move $b^{2}$ .

$10 a^{9} (b^{2} b^{6}) \cdot 3 - 7 a^{9} b^{8}$

Step 1.2.2

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

$10 a^{9} b^{2 + 6} \cdot 3 - 7 a^{9} b^{8}$

Step 1.2.3

Add $2$ and $6$ .

$10 a^{9} b^{8} \cdot 3 - 7 a^{9} b^{8}$

Step 1.3

Multiply $3$ by $10$ .

$30 a^{9} b^{8} - 7 a^{9} b^{8}$

Step 2

Subtract $7 a^{9} b^{8}$ from $30 a^{9} b^{8}$ .

$23 a^{9} b^{8}$