Simplify (3x-4y^2)(3x+4y^2)

$(3 x - 4 y^{2}) (3 x + 4 y^{2})$

Step 1

Expand $(3 x - 4 y^{2}) (3 x + 4 y^{2})$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 4 y^{2}) - 4 y^{2} (3 x + 4 y^{2})$

Apply the distributive property.

$3 x (3 x) + 3 x (4 y^{2}) - 4 y^{2} (3 x + 4 y^{2})$

Apply the distributive property.

$3 x (3 x) + 3 x (4 y^{2}) - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x (4 y^{2}) - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x (4 y^{2}) - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x (4 y^{2}) - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x (4 y^{2}) - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 \cdot 4 x y^{2} - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

Multiply $3$ by $4$ .

$9 x^{2} + 12 x y^{2} - 4 y^{2} (3 x) - 4 y^{2} (4 y^{2})$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 12 x y^{2} - 4 \cdot 3 y^{2} x - 4 y^{2} (4 y^{2})$

Multiply $- 4$ by $3$ .

$9 x^{2} + 12 x y^{2} - 12 y^{2} x - 4 y^{2} (4 y^{2})$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 12 x y^{2} - 12 y^{2} x - 4 \cdot 4 y^{2} y^{2}$

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

Move $y^{2}$ .

$9 x^{2} + 12 x y^{2} - 12 y^{2} x - 4 \cdot 4 (y^{2} y^{2})$

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

$9 x^{2} + 12 x y^{2} - 12 y^{2} x - 4 \cdot 4 y^{2 + 2}$

Add $2$ and $2$ .

$9 x^{2} + 12 x y^{2} - 12 y^{2} x - 4 \cdot 4 y^{4}$

Multiply $- 4$ by $4$ .

$9 x^{2} + 12 x y^{2} - 12 y^{2} x - 16 y^{4}$

Subtract $12 y^{2} x$ from $12 x y^{2}$ .

Move $y^{2}$ .

$9 x^{2} + 12 x y^{2} - 12 x y^{2} - 16 y^{4}$

Subtract $12 x y^{2}$ from $12 x y^{2}$ .

$9 x^{2} + 0 - 16 y^{4}$

Add $9 x^{2}$ and $0$ .

$9 x^{2} - 16 y^{4}$

Simplify (3x-4y^2)(3x+4y^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.