Algebra Examples

$(3 x - 2 y) (3 x + 2 y)$

Step 1

Expand $(3 x - 2 y) (3 x + 2 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 x (3 x + 2 y) - 2 y (3 x + 2 y)$

Step 1.2

Apply the distributive property.

$3 x (3 x) + 3 x (2 y) - 2 y (3 x + 2 y)$

Step 1.3

Apply the distributive property.

$3 x (3 x) + 3 x (2 y) - 2 y (3 x) - 2 y (2 y)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $3 x (3 x) + 3 x (2 y) - 2 y (3 x) - 2 y (2 y)$ .

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Step 2.1.1

Reorder the factors in the terms $3 x (2 y)$ and $- 2 y (3 x)$ .

$3 x (3 x) + 2 \cdot 3 x y - 2 \cdot 3 x y - 2 y (2 y)$

Step 2.1.2

Subtract $2 \cdot 3 x y$ from $2 \cdot 3 x y$ .

$3 x (3 x) + 0 - 2 y (2 y)$

Step 2.1.3

Add $3 x (3 x)$ and $0$ .

$3 x (3 x) - 2 y (2 y)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x - 2 y (2 y)$

Step 2.2.2

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

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Step 2.2.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) - 2 y (2 y)$

Step 2.2.2.2

Multiply $x$ by $x$ .

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

Step 2.2.3

Multiply $3$ by $3$ .

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

Step 2.2.4

Rewrite using the commutative property of multiplication.

$9 x^{2} - 2 \cdot 2 y \cdot y$

Step 2.2.5

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

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Step 2.2.5.1

Move $y$ .

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

Step 2.2.5.2

Multiply $y$ by $y$ .

$9 x^{2} - 2 \cdot 2 y^{2}$

Step 2.2.6

Multiply $- 2$ by $2$ .

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