Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

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.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $3$ by $3$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

Step 2.1.5

Multiply $3$ by $4$ .

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

Step 2.1.6

Rewrite using the commutative property of multiplication.

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

Step 2.1.7

Multiply $- 4$ by $3$ .

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

Step 2.1.8

Rewrite using the commutative property of multiplication.

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

Step 2.1.9

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

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Step 2.1.9.1

Move $y^{2}$ .

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

Step 2.1.9.2

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

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

Step 2.1.9.3

Add $2$ and $2$ .

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

Step 2.1.10

Multiply $- 4$ by $4$ .

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

Step 2.2

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

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Step 2.2.1

Move $y^{2}$ .

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

Step 2.2.2

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

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

Step 2.3

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

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