Basic Math Examples

$a^{6} + \frac{b^{6}}{a^{2} + b^{2}}$

Step 1

To write $a^{6}$ as a fraction with a common denominator, multiply by $\frac{a^{2} + b^{2}}{a^{2} + b^{2}}$ .

$\frac{a^{6} (a^{2} + b^{2})}{a^{2} + b^{2}} + \frac{b^{6}}{a^{2} + b^{2}}$

Step 2

Combine the numerators over the common denominator.

$\frac{a^{6} (a^{2} + b^{2}) + b^{6}}{a^{2} + b^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{a^{6} a^{2} + a^{6} b^{2} + b^{6}}{a^{2} + b^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{a^{6 + 2} + a^{6} b^{2} + b^{6}}{a^{2} + b^{2}}$

Step 3.2.2

Add $6$ and $2$ .

$\frac{a^{8} + a^{6} b^{2} + b^{6}}{a^{2} + b^{2}}$