Algebra Examples

$2 {(x - 3)}^{2} = 0$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 2

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

$2 ((x - 3) (x - 3)) = 0$

Step 3

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

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Step 3.1

Apply the distributive property.

$2 (x (x - 3) - 3 (x - 3)) = 0$

Step 3.2

Apply the distributive property.

$2 (x \cdot x + x \cdot - 3 - 3 (x - 3)) = 0$

Step 3.3

Apply the distributive property.

$2 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) = 0$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ .

$2 (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3) = 0$

Step 4.1.2

Move $- 3$ to the left of $x$ .

$2 (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3) = 0$

Step 4.1.3

Multiply $- 3$ by $- 3$ .

$2 (x^{2} - 3 x - 3 x + 9) = 0$

Step 4.2

Subtract $3 x$ from $- 3 x$ .

$2 (x^{2} - 6 x + 9) = 0$

Step 5

Apply the distributive property.

$2 x^{2} + 2 (- 6 x) + 2 \cdot 9 = 0$

Step 6

Simplify.

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Step 6.1

Multiply $- 6$ by $2$ .

$2 x^{2} - 12 x + 2 \cdot 9 = 0$

Step 6.2

Multiply $2$ by $9$ .

$2 x^{2} - 12 x + 18 = 0$

Step 7