Simplify (10+y^2)(10-y^2)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

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.

Simplify each term.

Multiply $10$ by $10$ .

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

Multiply $- 1$ by $10$ .

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

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

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

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

$100 + 0 - y^{4}$

Add $100$ and $0$ .

$100 - y^{4}$