Algebra Examples

$(10 + y^{2}) (10 - y^{2})$

Step 1

Expand $(10 + y^{2}) (10 - y^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$10 (10 - y^{2}) + y^{2} (10 - y^{2})$

Step 1.2

Apply the distributive property.

$10 \cdot 10 + 10 (- y^{2}) + y^{2} (10 - y^{2})$

Step 1.3

Apply the distributive property.

$10 \cdot 10 + 10 (- y^{2}) + y^{2} \cdot 10 + y^{2} (- y^{2})$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $10$ by $10$ .

$100 + 10 (- y^{2}) + y^{2} \cdot 10 + y^{2} (- y^{2})$

Step 2.1.2

Multiply $- 1$ by $10$ .

$100 - 10 y^{2} + y^{2} \cdot 10 + y^{2} (- y^{2})$

Step 2.1.3

Move $10$ to the left of $y^{2}$ .

$100 - 10 y^{2} + 10 \cdot y^{2} + y^{2} (- y^{2})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$100 - 10 y^{2} + 10 y^{2} - y^{2} y^{2}$

Step 2.1.5

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

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Step 2.1.5.1

Move $y^{2}$ .

$100 - 10 y^{2} + 10 y^{2} - (y^{2} y^{2})$

Step 2.1.5.2

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

$100 - 10 y^{2} + 10 y^{2} - y^{2 + 2}$

Step 2.1.5.3

Add $2$ and $2$ .

$100 - 10 y^{2} + 10 y^{2} - y^{4}$

Step 2.2

Add $- 10 y^{2}$ and $10 y^{2}$ .

$100 + 0 - y^{4}$

Step 2.3

Add $100$ and $0$ .

$100 - y^{4}$