Algebra Examples

(2 x - 3) (3 x + 4)

$(2 x - 3) (3 x + 4)$

Step 1

Expand

(2 x - 3) (3 x + 4)

$(2 x - 3) (3 x + 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 x (3 x + 4) - 3 (3 x + 4)

$2 x (3 x + 4) - 3 (3 x + 4)$

Step 1.2

Apply the distributive property.

2 x (3 x) + 2 x \cdot 4 - 3 (3 x + 4)

$2 x (3 x) + 2 x \cdot 4 - 3 (3 x + 4)$

Step 1.3

Apply the distributive property.

2 x (3 x) + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4

$2 x (3 x) + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4$

2 x (3 x) + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4

$2 x (3 x) + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4$

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.

2 \cdot 3 x \cdot x + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4

$2 \cdot 3 x \cdot x + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4$

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

$x$ .

2 \cdot 3 (x \cdot x) + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4

$2 \cdot 3 (x \cdot x) + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4$

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.1.3

Multiply

2

$2$ by

3

$3$ .

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

$6 x^{2} + 2 x \cdot 4 - 3 (3 x) - 3 \cdot 4$

Step 2.1.4

Multiply

4

$4$ by

2

$2$ .

6 x^{2} + 8 x - 3 (3 x) - 3 \cdot 4

$6 x^{2} + 8 x - 3 (3 x) - 3 \cdot 4$

Step 2.1.5

Multiply

3

$3$ by

- 3

$- 3$ .

6 x^{2} + 8 x - 9 x - 3 \cdot 4

$6 x^{2} + 8 x - 9 x - 3 \cdot 4$

Step 2.1.6

Multiply

- 3

$- 3$ by

4

$4$ .

6 x^{2} + 8 x - 9 x - 12

$6 x^{2} + 8 x - 9 x - 12$

6 x^{2} + 8 x - 9 x - 12

$6 x^{2} + 8 x - 9 x - 12$

Step 2.2

Subtract

9 x

$9 x$ from

8 x

$8 x$ .

6 x^{2} - x - 12

$6 x^{2} - x - 12$

6 x^{2} - x - 12

$6 x^{2} - x - 12$