Algebra Examples

$(g^{3} - h) (g^{3} + h)$

Step 1

Expand $(g^{3} - h) (g^{3} + h)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$g^{3} (g^{3} + h) - h (g^{3} + h)$

Step 1.2

Apply the distributive property.

$g^{3} g^{3} + g^{3} h - h (g^{3} + h)$

Step 1.3

Apply the distributive property.

$g^{3} g^{3} + g^{3} h - h g^{3} - h \cdot h$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $g^{3} g^{3} + g^{3} h - h g^{3} - h \cdot h$ .

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Step 2.1.1

Reorder the factors in the terms $g^{3} h$ and $- h g^{3}$ .

$g^{3} g^{3} + g^{3} h - g^{3} h - h \cdot h$

Step 2.1.2

Subtract $g^{3} h$ from $g^{3} h$ .

$g^{3} g^{3} + 0 - h \cdot h$

Step 2.1.3

Add $g^{3} g^{3}$ and $0$ .

$g^{3} g^{3} - h \cdot h$

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

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

$g^{3 + 3} - h \cdot h$

Step 2.2.1.2

Add $3$ and $3$ .

$g^{6} - h \cdot h$

Step 2.2.2

Multiply $h$ by $h$ by adding the exponents.

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Step 2.2.2.1

Move $h$ .

$g^{6} - (h \cdot h)$

Step 2.2.2.2

Multiply $h$ by $h$ .

$g^{6} - h^{2}$