Algebra Examples

{(3 x - 1)}^{2}

${(3 x - 1)}^{2}$

Step 1

Rewrite

{(3 x - 1)}^{2}

${(3 x - 1)}^{2}$ as

(3 x - 1) (3 x - 1)

$(3 x - 1) (3 x - 1)$ .

(3 x - 1) (3 x - 1)

$(3 x - 1) (3 x - 1)$

Step 2

Expand

(3 x - 1) (3 x - 1)

$(3 x - 1) (3 x - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

3 x (3 x - 1) - 1 (3 x - 1)

$3 x (3 x - 1) - 1 (3 x - 1)$

Step 2.2

Apply the distributive property.

3 x (3 x) + 3 x \cdot - 1 - 1 (3 x - 1)

$3 x (3 x) + 3 x \cdot - 1 - 1 (3 x - 1)$

Step 2.3

Apply the distributive property.

3 x (3 x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1

$3 x (3 x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1$

3 x (3 x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1

$3 x (3 x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1$

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 - 1 - 1 (3 x) - 1 \cdot - 1

$3 \cdot 3 x \cdot x + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1$

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

$x$ .

3 \cdot 3 (x \cdot x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1

$3 \cdot 3 (x \cdot x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1$

Step 3.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 3.1.3

Multiply

3

$3$ by

3

$3$ .

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

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

Step 3.1.4

Multiply

- 1

$- 1$ by

3

$3$ .

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

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

Step 3.1.5

Multiply

3

$3$ by

- 1

$- 1$ .

9 x^{2} - 3 x - 3 x - 1 \cdot - 1

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

Step 3.1.6

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

9 x^{2} - 3 x - 3 x + 1

$9 x^{2} - 3 x - 3 x + 1$

9 x^{2} - 3 x - 3 x + 1

$9 x^{2} - 3 x - 3 x + 1$

Step 3.2

Subtract

3 x

$3 x$ from

- 3 x

$- 3 x$ .

9 x^{2} - 6 x + 1

$9 x^{2} - 6 x + 1$

9 x^{2} - 6 x + 1

$9 x^{2} - 6 x + 1$