Find the Product (x+y^2)(x-y^2)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- y^{2}) + y^{2} x + y^{2} (- y^{2})$ .

Reorder the factors in the terms $x (- y^{2})$ and $y^{2} x$ .

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

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

$x \cdot x + 0 + y^{2} (- y^{2})$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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