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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $10$ by $10$ .

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

Rewrite using the commutative property of multiplication.

$100 x^{2} + 10 \cdot - 1 x y^{2} + y^{2} (10 x) + y^{2} (- y^{2})$

Multiply $10$ by $- 1$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $y^{2}$ .

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

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

$100 x^{2} + 0 - y^{4}$

Add $100 x^{2}$ and $0$ .

$100 x^{2} - y^{4}$