Algebra Examples

(3 x + 4 y) (3 x - 4 y)

$(3 x + 4 y) (3 x - 4 y)$

Step 1

Expand

(3 x + 4 y) (3 x - 4 y)

$(3 x + 4 y) (3 x - 4 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

3 x (3 x - 4 y) + 4 y (3 x - 4 y)

$3 x (3 x - 4 y) + 4 y (3 x - 4 y)$

Step 1.2

Apply the distributive property.

3 x (3 x) + 3 x (- 4 y) + 4 y (3 x - 4 y)

$3 x (3 x) + 3 x (- 4 y) + 4 y (3 x - 4 y)$

Step 1.3

Apply the distributive property.

3 x (3 x) + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)

$3 x (3 x) + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)$

3 x (3 x) + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)

$3 x (3 x) + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)$

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) + 4 y (3 x) + 4 y (- 4 y)

$3 \cdot 3 x \cdot x + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)$

Step 2.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.2.1

Move

x

$x$ .

3 \cdot 3 (x \cdot x) + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)

$3 \cdot 3 (x \cdot x) + 3 x (- 4 y) + 4 y (3 x) + 4 y (- 4 y)$

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.1.3

Multiply

3

$3$ by

3

$3$ .

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

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

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

Step 2.1.5

Multiply

3

$3$ by

- 4

$- 4$ .

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

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

Step 2.1.6

Rewrite using the commutative property of multiplication.

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

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

Step 2.1.7

Multiply

4

$4$ by

3

$3$ .

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

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

Step 2.1.8

Rewrite using the commutative property of multiplication.

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

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

Step 2.1.9

Multiply

y

$y$ by

y

$y$ by adding the exponents.

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Step 2.1.9.1

Move

y

$y$ .

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

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

Step 2.1.9.2

Multiply

y

$y$ by

y

$y$ .

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

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

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

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

Step 2.1.10

Multiply

4

$4$ by

- 4

$- 4$ .

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

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

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

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

Step 2.2

Add

- 12 x y

$- 12 x y$ and

12 y x

$12 y x$ .

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Step 2.2.1

Move

y

$y$ .

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

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

Step 2.2.2

Add

- 12 x y

$- 12 x y$ and

12 x y

$12 x y$ .

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

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

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

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

Step 2.3

Add

9 x^{2}

$9 x^{2}$ and

0

$0$ .

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

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

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

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