Algebra Examples

{(2 x - 6)}^{2}

${(2 x - 6)}^{2}$

Step 1

Rewrite

{(2 x - 6)}^{2}

${(2 x - 6)}^{2}$ as

(2 x - 6) (2 x - 6)

$(2 x - 6) (2 x - 6)$ .

(2 x - 6) (2 x - 6)

$(2 x - 6) (2 x - 6)$

Step 2

Expand

(2 x - 6) (2 x - 6)

$(2 x - 6) (2 x - 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

2 x (2 x - 6) - 6 (2 x - 6)

$2 x (2 x - 6) - 6 (2 x - 6)$

Step 2.2

Apply the distributive property.

2 x (2 x) + 2 x \cdot - 6 - 6 (2 x - 6)

$2 x (2 x) + 2 x \cdot - 6 - 6 (2 x - 6)$

Step 2.3

Apply the distributive property.

2 x (2 x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

$2 x (2 x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

2 x (2 x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

$2 x (2 x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

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 2 x \cdot x + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

$2 \cdot 2 x \cdot x + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

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

$x$ .

2 \cdot 2 (x \cdot x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

Step 3.1.2.2

Multiply

x

$x$ by

x

$x$ .

2 \cdot 2 x^{2} + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

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

2 \cdot 2 x^{2} + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

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

Step 3.1.3

Multiply

2

$2$ by

2

$2$ .

4 x^{2} + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6

$4 x^{2} + 2 x \cdot - 6 - 6 (2 x) - 6 \cdot - 6$

Step 3.1.4

Multiply

- 6

$- 6$ by

2

$2$ .

4 x^{2} - 12 x - 6 (2 x) - 6 \cdot - 6

$4 x^{2} - 12 x - 6 (2 x) - 6 \cdot - 6$

Step 3.1.5

Multiply

2

$2$ by

- 6

$- 6$ .

4 x^{2} - 12 x - 12 x - 6 \cdot - 6

$4 x^{2} - 12 x - 12 x - 6 \cdot - 6$

Step 3.1.6

Multiply

- 6

$- 6$ by

- 6

$- 6$ .

4 x^{2} - 12 x - 12 x + 36

$4 x^{2} - 12 x - 12 x + 36$

4 x^{2} - 12 x - 12 x + 36

$4 x^{2} - 12 x - 12 x + 36$

Step 3.2

Subtract

12 x

$12 x$ from

- 12 x

$- 12 x$ .

4 x^{2} - 24 x + 36

$4 x^{2} - 24 x + 36$

4 x^{2} - 24 x + 36

$4 x^{2} - 24 x + 36$