Algebra Examples

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

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

Step 1

Rewrite

{(x - 1)}^{2}

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

(x - 1) (x - 1)

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

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

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

Step 2

Expand

(x - 1) (x - 1)

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

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Step 2.1

Apply the distributive property.

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

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

Step 2.2

Apply the distributive property.

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

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

Step 2.3

Apply the distributive property.

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

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

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

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

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

Multiply

x

$x$ by

x

$x$ .

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

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

Step 3.1.2

Move

- 1

$- 1$ to the left of

x

$x$ .

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

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

Step 3.1.3

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

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

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

Step 3.1.4

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

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

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

Step 3.1.5

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

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

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

Step 3.2

Subtract

x

$x$ from

- x

$- x$ .

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

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

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

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

Step 4

Apply the distributive property.

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

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

Step 5

Simplify.

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Step 5.1

Multiply

- 2

$- 2$ by

3

$3$ .

3 x^{2} - 6 x + 3 \cdot 1

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

Step 5.2

Multiply

3

$3$ by

1

$1$ .

3 x^{2} - 6 x + 3

$3 x^{2} - 6 x + 3$

3 x^{2} - 6 x + 3

$3 x^{2} - 6 x + 3$

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

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

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$