Algebra Examples

${(1 - \frac{y^{4}}{16})}^{2}$

Step 1

Rewrite ${(1 - \frac{y^{4}}{16})}^{2}$ as $(1 - \frac{y^{4}}{16}) (1 - \frac{y^{4}}{16})$ .

$(1 - \frac{y^{4}}{16}) (1 - \frac{y^{4}}{16})$

Step 2

Expand $(1 - \frac{y^{4}}{16}) (1 - \frac{y^{4}}{16})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$1 (1 - \frac{y^{4}}{16}) - \frac{y^{4}}{16} (1 - \frac{y^{4}}{16})$

Step 2.2

Apply the distributive property.

$1 \cdot 1 + 1 (- \frac{y^{4}}{16}) - \frac{y^{4}}{16} (1 - \frac{y^{4}}{16})$

Step 2.3

Apply the distributive property.

$1 \cdot 1 + 1 (- \frac{y^{4}}{16}) - \frac{y^{4}}{16} \cdot 1 - \frac{y^{4}}{16} (- \frac{y^{4}}{16})$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $1$ by $1$ .

$1 + 1 (- \frac{y^{4}}{16}) - \frac{y^{4}}{16} \cdot 1 - \frac{y^{4}}{16} (- \frac{y^{4}}{16})$

Step 3.1.2

Multiply $- \frac{y^{4}}{16}$ by $1$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} \cdot 1 - \frac{y^{4}}{16} (- \frac{y^{4}}{16})$

Step 3.1.3

Multiply $- 1$ by $1$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} - \frac{y^{4}}{16} (- \frac{y^{4}}{16})$

Step 3.1.4

Multiply $- \frac{y^{4}}{16} (- \frac{y^{4}}{16})$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} + 1 \frac{y^{4}}{16} \frac{y^{4}}{16}$

Step 3.1.4.2

Multiply $\frac{y^{4}}{16}$ by $1$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} + \frac{y^{4}}{16} \cdot \frac{y^{4}}{16}$

Step 3.1.4.3

Multiply $\frac{y^{4}}{16}$ by $\frac{y^{4}}{16}$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} + \frac{y^{4} y^{4}}{16 \cdot 16}$

Step 3.1.4.4

Multiply $y^{4}$ by $y^{4}$ by adding the exponents.

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Step 3.1.4.4.1

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

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} + \frac{y^{4 + 4}}{16 \cdot 16}$

Step 3.1.4.4.2

Add $4$ and $4$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} + \frac{y^{8}}{16 \cdot 16}$

Step 3.1.4.5

Multiply $16$ by $16$ .

$1 - \frac{y^{4}}{16} - \frac{y^{4}}{16} + \frac{y^{8}}{256}$

Step 3.2

Subtract $\frac{y^{4}}{16}$ from $- \frac{y^{4}}{16}$ .

$1 - 2 \frac{y^{4}}{16} + \frac{y^{8}}{256}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $- 2$ .

$1 + 2 (- 1) \frac{y^{4}}{16} + \frac{y^{8}}{256}$

Step 4.1.2

Factor $2$ out of $16$ .

$1 + 2 \cdot - 1 \frac{y^{4}}{2 \cdot 8} + \frac{y^{8}}{256}$

Step 4.1.3

Cancel the common factor.

$1 + 2 \cdot - 1 \frac{y^{4}}{2 \cdot 8} + \frac{y^{8}}{256}$

Step 4.1.4

Rewrite the expression.

$1 - 1 \frac{y^{4}}{8} + \frac{y^{8}}{256}$

Step 4.2

Rewrite $- 1 \frac{y^{4}}{8}$ as $- \frac{y^{4}}{8}$ .

$1 - \frac{y^{4}}{8} + \frac{y^{8}}{256}$