Find the Product (9y^2-4x)(9y^2+4x)

$(9 y^{2} - 4 x) (9 y^{2} + 4 x)$

Step 1

Expand $(9 y^{2} - 4 x) (9 y^{2} + 4 x)$ using the FOIL Method.

Apply the distributive property.

$9 y^{2} (9 y^{2} + 4 x) - 4 x (9 y^{2} + 4 x)$

Apply the distributive property.

$9 y^{2} (9 y^{2}) + 9 y^{2} (4 x) - 4 x (9 y^{2} + 4 x)$

Apply the distributive property.

$9 y^{2} (9 y^{2}) + 9 y^{2} (4 x) - 4 x (9 y^{2}) - 4 x (4 x)$

Step 2

Simplify terms.

Combine the opposite terms in $9 y^{2} (9 y^{2}) + 9 y^{2} (4 x) - 4 x (9 y^{2}) - 4 x (4 x)$ .

Reorder the factors in the terms $9 y^{2} (4 x)$ and $- 4 x (9 y^{2})$ .

$9 y^{2} (9 y^{2}) + 4 \cdot 9 y^{2} x - 4 \cdot 9 y^{2} x - 4 x (4 x)$

Subtract $4 \cdot 9 y^{2} x$ from $4 \cdot 9 y^{2} x$ .

$9 y^{2} (9 y^{2}) + 0 - 4 x (4 x)$

Add $9 y^{2} (9 y^{2})$ and $0$ .

$9 y^{2} (9 y^{2}) - 4 x (4 x)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 \cdot 9 y^{2} y^{2} - 4 x (4 x)$

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

Move $y^{2}$ .

$9 \cdot 9 (y^{2} y^{2}) - 4 x (4 x)$

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

$9 \cdot 9 y^{2 + 2} - 4 x (4 x)$

Add $2$ and $2$ .

$9 \cdot 9 y^{4} - 4 x (4 x)$

Multiply $9$ by $9$ .

$81 y^{4} - 4 x (4 x)$

Rewrite using the commutative property of multiplication.

$81 y^{4} - 4 \cdot 4 x \cdot x$

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

Move $x$ .

$81 y^{4} - 4 \cdot 4 (x \cdot x)$

Multiply $x$ by $x$ .

$81 y^{4} - 4 \cdot 4 x^{2}$

Multiply $- 4$ by $4$ .

$81 y^{4} - 16 x^{2}$