Pre-Algebra Examples

$2 x + 1$ , $3 x + 9$

Step 1

Multiply the expressions.

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $x$ .

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

Step 3.1.2.2

Multiply $x$ by $x$ .

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

Step 3.1.3

Multiply $2$ by $3$ .

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

Step 3.1.4

Multiply $9$ by $2$ .

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

Step 3.1.5

Multiply $3 x$ by $1$ .

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

Step 3.1.6

Multiply $9$ by $1$ .

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

Step 3.2

Add $18 x$ and $3 x$ .

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

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