Basic Math Examples

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

Step 1

Expand $(p^{5} + q^{3}) (p^{5} + q^{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$p^{5} p^{5} + p^{5} q^{3} + q^{3} p^{5} + q^{3} q^{3}$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

$p^{5 + 5} + p^{5} q^{3} + q^{3} p^{5} + q^{3} q^{3}$

Step 2.1.1.2

Add $5$ and $5$ .

$p^{10} + p^{5} q^{3} + q^{3} p^{5} + q^{3} q^{3}$

Step 2.1.2

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

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Step 2.1.2.1

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

$p^{10} + p^{5} q^{3} + q^{3} p^{5} + q^{3 + 3}$

Step 2.1.2.2

Add $3$ and $3$ .

$p^{10} + p^{5} q^{3} + q^{3} p^{5} + q^{6}$

Step 2.2

Add $p^{5} q^{3}$ and $q^{3} p^{5}$ .

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Step 2.2.1

Reorder $q^{3}$ and $p^{5}$ .

$p^{10} + p^{5} q^{3} + p^{5} q^{3} + q^{6}$

Step 2.2.2

Add $p^{5} q^{3}$ and $p^{5} q^{3}$ .

$p^{10} + 2 p^{5} q^{3} + q^{6}$