Algebra Examples

${(3 x + 2)}^{2}$

Step 1

Rewrite ${(3 x + 2)}^{2}$ as $(3 x + 2) (3 x + 2)$ .

$(3 x + 2) (3 x + 2)$

Step 2

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

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Step 2.1

Apply the distributive property.

$3 x (3 x + 2) + 2 (3 x + 2)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $x$ .

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

Step 3.1.2.2

Multiply $x$ by $x$ .

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

Step 3.1.3

Multiply $3$ by $3$ .

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

Step 3.1.4

Multiply $2$ by $3$ .

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

Step 3.1.5

Multiply $3$ by $2$ .

$9 x^{2} + 6 x + 6 x + 2 \cdot 2$

Step 3.1.6

Multiply $2$ by $2$ .

$9 x^{2} + 6 x + 6 x + 4$

Step 3.2

Add $6 x$ and $6 x$ .

$9 x^{2} + 12 x + 4$