Algebra Examples

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

${(9 x - 2)}^{2}$

Step 1

Rewrite

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

${(9 x - 2)}^{2}$ as

(9 x - 2) (9 x - 2)

$(9 x - 2) (9 x - 2)$ .

(9 x - 2) (9 x - 2)

$(9 x - 2) (9 x - 2)$

Step 2

Expand

(9 x - 2) (9 x - 2)

$(9 x - 2) (9 x - 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

9 x (9 x - 2) - 2 (9 x - 2)

$9 x (9 x - 2) - 2 (9 x - 2)$

Step 2.2

Apply the distributive property.

9 x (9 x) + 9 x \cdot - 2 - 2 (9 x - 2)

$9 x (9 x) + 9 x \cdot - 2 - 2 (9 x - 2)$

Step 2.3

Apply the distributive property.

9 x (9 x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2

$9 x (9 x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2$

9 x (9 x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2

$9 x (9 x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2$

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.

9 \cdot 9 x \cdot x + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2

$9 \cdot 9 x \cdot x + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2$

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

$x$ .

9 \cdot 9 (x \cdot x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2

$9 \cdot 9 (x \cdot x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2$

Step 3.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 3.1.3

Multiply

9

$9$ by

9

$9$ .

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

$81 x^{2} + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2$

Step 3.1.4

Multiply

- 2

$- 2$ by

9

$9$ .

81 x^{2} - 18 x - 2 (9 x) - 2 \cdot - 2

$81 x^{2} - 18 x - 2 (9 x) - 2 \cdot - 2$

Step 3.1.5

Multiply

9

$9$ by

- 2

$- 2$ .

81 x^{2} - 18 x - 18 x - 2 \cdot - 2

$81 x^{2} - 18 x - 18 x - 2 \cdot - 2$

Step 3.1.6

Multiply

- 2

$- 2$ by

- 2

$- 2$ .

81 x^{2} - 18 x - 18 x + 4

$81 x^{2} - 18 x - 18 x + 4$

81 x^{2} - 18 x - 18 x + 4

$81 x^{2} - 18 x - 18 x + 4$

Step 3.2

Subtract

18 x

$18 x$ from

- 18 x

$- 18 x$ .

81 x^{2} - 36 x + 4

$81 x^{2} - 36 x + 4$

81 x^{2} - 36 x + 4

$81 x^{2} - 36 x + 4$