Algebra Examples

$(3 x + \frac{1}{3}) (3 x - \frac{1}{3})$

Step 1

Expand $(3 x + \frac{1}{3}) (3 x - \frac{1}{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 x (3 x - \frac{1}{3}) + \frac{1}{3} (3 x - \frac{1}{3})$

Step 1.2

Apply the distributive property.

$3 x (3 x) + 3 x (- \frac{1}{3}) + \frac{1}{3} (3 x - \frac{1}{3})$

Step 1.3

Apply the distributive property.

$3 x (3 x) + 3 x (- \frac{1}{3}) + \frac{1}{3} (3 x) + \frac{1}{3} (- \frac{1}{3})$

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.

$3 \cdot 3 x \cdot x + 3 x (- \frac{1}{3}) + \frac{1}{3} (3 x) + \frac{1}{3} (- \frac{1}{3})$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x (- \frac{1}{3}) + \frac{1}{3} (3 x) + \frac{1}{3} (- \frac{1}{3})$

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $3$ by $3$ .

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

Step 2.1.4

Cancel the common factor of $3$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Step 2.1.4.2

Factor $3$ out of $3 x$ .

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

Step 2.1.4.3

Cancel the common factor.

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

Step 2.1.4.4

Rewrite the expression.

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

Step 2.1.5

Move $- 1$ to the left of $x$ .

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

Step 2.1.6

Rewrite $- 1 x$ as $- x$ .

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

Step 2.1.7

Cancel the common factor of $3$ .

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Step 2.1.7.1

Factor $3$ out of $3 x$ .

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

Step 2.1.7.2

Cancel the common factor.

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

Step 2.1.7.3

Rewrite the expression.

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

Step 2.1.8

Multiply $\frac{1}{3} (- \frac{1}{3})$ .

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Step 2.1.8.1

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

$9 x^{2} - x + x - \frac{1}{3 \cdot 3}$

Step 2.1.8.2

Multiply $3$ by $3$ .

$9 x^{2} - x + x - \frac{1}{9}$

Step 2.2

Add $- x$ and $x$ .

$9 x^{2} + 0 - \frac{1}{9}$

Step 2.3

Add $9 x^{2}$ and $0$ .

$9 x^{2} - \frac{1}{9}$