Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $1$ .

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

Step 3.1.2

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

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

Step 3.1.3

Multiply $- 1$ by $1$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

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

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Step 3.1.5.1

Move $y^{2}$ .

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

Step 3.1.5.2

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

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

Step 3.1.5.3

Add $2$ and $2$ .

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

Step 3.1.6

Multiply $- 1$ by $- 1$ .

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

Step 3.1.7

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

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

Step 3.2

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

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