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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

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

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

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

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

Simplify each term.

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

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

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

Add $2$ and $2$ .

$x^{4} + 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$x^{4} + 2 \cdot - 2 y \cdot y$

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

Move $y$ .

$x^{4} + 2 \cdot - 2 (y \cdot y)$

Multiply $y$ by $y$ .

$x^{4} + 2 \cdot - 2 y^{2}$

Multiply $2$ by $- 2$ .

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