Simplify (1-y^2)^2

${(1 - y^{2})}^{2}$

Rewrite ${(1 - y^{2})}^{2}$ as $(1 - y^{2}) (1 - y^{2})$ .

$(1 - y^{2}) (1 - y^{2})$

Expand $(1 - y^{2}) (1 - y^{2})$ using the FOIL Method.

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Apply the distributive property.

$1 (1 - y^{2}) - y^{2} (1 - y^{2})$

Apply the distributive property.

$1 \cdot 1 + 1 (- y^{2}) - y^{2} (1 - y^{2})$

Apply the distributive property.

$1 \cdot 1 + 1 (- y^{2}) - y^{2} \cdot 1 - y^{2} (- y^{2})$

Simplify and combine like terms.

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Simplify each term.

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Multiply $1$ by $1$ .

$1 + 1 (- y^{2}) - y^{2} \cdot 1 - y^{2} (- y^{2})$

Multiply $- y^{2}$ by $1$ .

$1 - y^{2} - y^{2} \cdot 1 - y^{2} (- y^{2})$

Multiply $- 1$ by $1$ .

$1 - y^{2} - y^{2} - y^{2} (- y^{2})$

Rewrite using the commutative property of multiplication.

$1 - y^{2} - y^{2} - 1 \cdot - 1 (y^{2} y^{2})$

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

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

$1 - y^{2} - y^{2} - 1 \cdot - 1 y^{2 + 2}$

Add $2$ and $2$ .

$1 - y^{2} - y^{2} - 1 \cdot - 1 y^{4}$

Multiply $- 1$ by $- 1$ .

$1 - y^{2} - y^{2} + 1 y^{4}$

Multiply $y^{4}$ by $1$ .

$1 - y^{2} - y^{2} + y^{4}$

Subtract $y^{2}$ from $- y^{2}$ .

$1 - 2 y^{2} + y^{4}$

Simplify (1-y^2)^2

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