Algebra Examples

2 x + 1

$2 x + 1$ ,

3 x + 9

$3 x + 9$

Step 1

Multiply the expressions.

(2 x + 1) \cdot (3 x + 9)

$(2 x + 1) \cdot (3 x + 9)$

Step 2

Expand

(2 x + 1) (3 x + 9)

$(2 x + 1) (3 x + 9)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

2 x (3 x + 9) + 1 (3 x + 9)

$2 x (3 x + 9) + 1 (3 x + 9)$

Step 2.2

Apply the distributive property.

2 x (3 x) + 2 x \cdot 9 + 1 (3 x + 9)

$2 x (3 x) + 2 x \cdot 9 + 1 (3 x + 9)$

Step 2.3

Apply the distributive property.

2 x (3 x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$2 x (3 x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

2 x (3 x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$2 x (3 x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

2 \cdot 3 x \cdot x + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$2 \cdot 3 x \cdot x + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Step 3.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 3.1.2.1

Move

x

$x$ .

2 \cdot 3 (x \cdot x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$2 \cdot 3 (x \cdot x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Step 3.1.2.2

Multiply

x

$x$ by

x

$x$ .

2 \cdot 3 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$2 \cdot 3 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

2 \cdot 3 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$2 \cdot 3 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Step 3.1.3

Multiply

2

$2$ by

3

$3$ .

6 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9

$6 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Step 3.1.4

Multiply

9

$9$ by

2

$2$ .

6 x^{2} + 18 x + 1 (3 x) + 1 \cdot 9

$6 x^{2} + 18 x + 1 (3 x) + 1 \cdot 9$

Step 3.1.5

Multiply

3 x

$3 x$ by

1

$1$ .

6 x^{2} + 18 x + 3 x + 1 \cdot 9

$6 x^{2} + 18 x + 3 x + 1 \cdot 9$

Step 3.1.6

Multiply

9

$9$ by

1

$1$ .

6 x^{2} + 18 x + 3 x + 9

$6 x^{2} + 18 x + 3 x + 9$

6 x^{2} + 18 x + 3 x + 9

$6 x^{2} + 18 x + 3 x + 9$

Step 3.2

Add

18 x

$18 x$ and

3 x

$3 x$ .

6 x^{2} + 21 x + 9

$6 x^{2} + 21 x + 9$

6 x^{2} + 21 x + 9

$6 x^{2} + 21 x + 9$

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