Simplify (10+y)(10-y)

$(10 + y) (10 - y)$

Step 1

Expand $(10 + y) (10 - y)$ using the FOIL Method.

Apply the distributive property.

$10 (10 - y) + y (10 - y)$

Apply the distributive property.

$10 \cdot 10 + 10 (- y) + y (10 - y)$

Apply the distributive property.

$10 \cdot 10 + 10 (- y) + y \cdot 10 + y (- y)$

$10 \cdot 10 + 10 (- y) + y \cdot 10 + y (- y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $10$ .

$100 + 10 (- y) + y \cdot 10 + y (- y)$

Multiply $- 1$ by $10$ .

$100 - 10 y + y \cdot 10 + y (- y)$

Move $10$ to the left of $y$ .

$100 - 10 y + 10 \cdot y + y (- y)$

Rewrite using the commutative property of multiplication.

$100 - 10 y + 10 y - y \cdot y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$100 - 10 y + 10 y - (y \cdot y)$

Multiply $y$ by $y$ .

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

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

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

Add $- 10 y$ and $10 y$ .

$100 + 0 - y^{2}$

Add $100$ and $0$ .

$100 - y^{2}$

$100 - y^{2}$

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