Algebra Examples

$p^{2} q^{3} (p^{5} q^{2} - p q)$

Step 1

Apply the distributive property.

$p^{2} q^{3} (p^{5} q^{2}) + p^{2} q^{3} (- p q)$

Step 2

Multiply $p^{2}$ by $p^{5}$ by adding the exponents.

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Step 2.1

Move $p^{5}$ .

$p^{5} p^{2} q^{3} q^{2} + p^{2} q^{3} (- p q)$

Step 2.2

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

$p^{5 + 2} q^{3} q^{2} + p^{2} q^{3} (- p q)$

Step 2.3

Add $5$ and $2$ .

$p^{7} q^{3} q^{2} + p^{2} q^{3} (- p q)$

Step 3

Rewrite using the commutative property of multiplication.

$p^{7} q^{3} q^{2} - p^{2} q^{3} (p q)$

Step 4

Simplify each term.

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Step 4.1

Multiply $q^{3}$ by $q^{2}$ by adding the exponents.

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Step 4.1.1

Move $q^{2}$ .

$p^{7} (q^{2} q^{3}) - p^{2} q^{3} (p q)$

Step 4.1.2

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

$p^{7} q^{2 + 3} - p^{2} q^{3} (p q)$

Step 4.1.3

Add $2$ and $3$ .

$p^{7} q^{5} - p^{2} q^{3} (p q)$

Step 4.2

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

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Step 4.2.1

Move $p$ .

$p^{7} q^{5} - (p \cdot p^{2}) q^{3} q$

Step 4.2.2

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

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Step 4.2.2.1

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

$p^{7} q^{5} - (p^{1} p^{2}) q^{3} q$

Step 4.2.2.2

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

$p^{7} q^{5} - p^{1 + 2} q^{3} q$

Step 4.2.3

Add $1$ and $2$ .

$p^{7} q^{5} - p^{3} q^{3} q$

Step 4.3

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

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Step 4.3.1

Move $q$ .

$p^{7} q^{5} - p^{3} (q \cdot q^{3})$

Step 4.3.2

Multiply $q$ by $q^{3}$ .

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Step 4.3.2.1

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

$p^{7} q^{5} - p^{3} (q^{1} q^{3})$

Step 4.3.2.2

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

$p^{7} q^{5} - p^{3} q^{1 + 3}$

Step 4.3.3

Add $1$ and $3$ .

$p^{7} q^{5} - p^{3} q^{4}$