Find the Product (x^2+4y^2)(x^2-4y^2)

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

Expand $(x^{2} + 4 y^{2}) (x^{2} - 4 y^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} (- 4 y^{2}) + 4 y^{2} x^{2} + 4 y^{2} (- 4 y^{2})$ .

Reorder the factors in the terms $x^{2} (- 4 y^{2})$ and $4 y^{2} x^{2}$ .

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

Add $- 4 x^{2} y^{2}$ and $4 x^{2} y^{2}$ .

$x^{2} x^{2} + 0 + 4 y^{2} (- 4 y^{2})$

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

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

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.

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $4$ by $- 4$ .

$x^{4} - 16 y^{4}$