Algebra Examples

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

Step 1

Rewrite

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

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

$2 ((x - 3) (x - 3))$

Step 2

Expand

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

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Step 2.1

Apply the distributive property.

$2 (x (x - 3) - 3 (x - 3))$

Step 2.2

Apply the distributive property.

$2 (x \cdot x + x \cdot - 3 - 3 (x - 3))$

Step 2.3

Apply the distributive property.

$2 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

$2 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

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

$x$ by

$x$ .

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

Step 3.1.2

Move

$- 3$ to the left of

$x$ .

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

Step 3.1.3

Multiply

$- 3$ by

$- 3$ .

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

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

Step 3.2

Subtract

$3 x$ from

$- 3 x$ .

$2 (x^{2} - 6 x + 9)$

$2 (x^{2} - 6 x + 9)$

Step 4

Apply the distributive property.

$2 x^{2} + 2 (- 6 x) + 2 \cdot 9$

Step 5

Simplify.

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Step 5.1

Multiply

$- 6$ by

$2$ .

$2 x^{2} - 12 x + 2 \cdot 9$

Step 5.2

Multiply

$2$ by

$9$ .

$2 x^{2} - 12 x + 18$

$2 x^{2} - 12 x + 18$

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