Basic Math Examples

$y^{100} y^{4} - 64^{2}$

Step 1

Rewrite $y^{100} y^{4}$ as ${(y^{50} y^{2})}^{2}$ .

${(y^{50} y^{2})}^{2} - 64^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y^{50} y^{2}$ and $b = 64$ .

$(y^{50} y^{2} + 64) (y^{50} y^{2} - 64)$

Step 3

Simplify.

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Step 3.1

Multiply $y^{50}$ by $y^{2}$ by adding the exponents.

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Step 3.1.1

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

$(y^{50 + 2} + 64) (y^{50} y^{2} - 64)$

Step 3.1.2

Add $50$ and $2$ .

$(y^{52} + 64) (y^{50} y^{2} - 64)$

Step 3.2

Rewrite $y^{50} y^{2}$ as ${(y^{25} y)}^{2}$ .

$(y^{52} + 64) ({(y^{25} y)}^{2} - 64)$

Step 3.3

Rewrite $64$ as $8^{2}$ .

$(y^{52} + 64) ({(y^{25} y)}^{2} - 8^{2})$

Step 3.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y^{25} y$ and $b = 8$ .

$(y^{52} + 64) ((y^{25} y + 8) (y^{25} y - 8))$

Step 3.5

Factor.

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Step 3.5.1

Simplify.

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Step 3.5.1.1

Multiply $y^{25}$ by $y$ by adding the exponents.

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Step 3.5.1.1.1

Multiply $y^{25}$ by $y$ .

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Step 3.5.1.1.1.1

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

$(y^{52} + 64) ((y^{25} y^{1} + 8) (y^{25} y - 8))$

Step 3.5.1.1.1.2

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

$(y^{52} + 64) ((y^{25 + 1} + 8) (y^{25} y - 8))$

Step 3.5.1.1.2

Add $25$ and $1$ .

$(y^{52} + 64) ((y^{26} + 8) (y^{25} y - 8))$

Step 3.5.1.2

Multiply $y^{25}$ by $y$ by adding the exponents.

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Step 3.5.1.2.1

Multiply $y^{25}$ by $y$ .

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Step 3.5.1.2.1.1

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

$(y^{52} + 64) ((y^{26} + 8) (y^{25} y^{1} - 8))$

Step 3.5.1.2.1.2

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

$(y^{52} + 64) ((y^{26} + 8) (y^{25 + 1} - 8))$

Step 3.5.1.2.2

Add $25$ and $1$ .

$(y^{52} + 64) ((y^{26} + 8) (y^{26} - 8))$

Step 3.5.2

Remove unnecessary parentheses.

$(y^{52} + 64) (y^{26} + 8) (y^{26} - 8)$