Simplify (1-(y^4)/16)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

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

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

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

Multiply $- 1$ by $1$ .

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

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

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

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

Add $4$ and $4$ .

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

Multiply $16$ by $16$ .

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

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

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

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify (1-(y^4)/16)^2

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