Algebra Examples

$9 m^{7} n \cdot 3 m^{2} n^{2} - 4 m^{4} \cdot 5 m^{5} n^{3}$

Step 1

Simplify each term.

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Step 1.1

Multiply $m^{7}$ by $m^{2}$ by adding the exponents.

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Step 1.1.1

Move $m^{2}$ .

$9 (m^{2} m^{7}) n \cdot (3 n^{2}) - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.1.2

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

$9 m^{2 + 7} n \cdot (3 n^{2}) - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.1.3

Add $2$ and $7$ .

$9 m^{9} n \cdot (3 n^{2}) - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.2

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

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Step 1.2.1

Move $n^{2}$ .

$9 m^{9} (n^{2} n) \cdot 3 - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.2.2

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

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Step 1.2.2.1

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

$9 m^{9} (n^{2} n^{1}) \cdot 3 - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.2.2.2

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

$9 m^{9} n^{2 + 1} \cdot 3 - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.2.3

Add $2$ and $1$ .

$9 m^{9} n^{3} \cdot 3 - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.3

Multiply $3$ by $9$ .

$27 m^{9} n^{3} - 4 m^{4} \cdot (5 m^{5} n^{3})$

Step 1.4

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

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Step 1.4.1

Move $m^{5}$ .

$27 m^{9} n^{3} - 4 (m^{5} m^{4}) \cdot (5 n^{3})$

Step 1.4.2

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

$27 m^{9} n^{3} - 4 m^{5 + 4} \cdot (5 n^{3})$

Step 1.4.3

Add $5$ and $4$ .

$27 m^{9} n^{3} - 4 m^{9} \cdot (5 n^{3})$

Step 1.5

Rewrite using the commutative property of multiplication.

$27 m^{9} n^{3} - 4 \cdot 5 m^{9} n^{3}$

Step 1.6

Multiply $- 4$ by $5$ .

$27 m^{9} n^{3} - 20 m^{9} n^{3}$

Step 2

Subtract $20 m^{9} n^{3}$ from $27 m^{9} n^{3}$ .

$7 m^{9} n^{3}$