Algebra Examples

${(x + 2)}^{2} = 3 (x + 2)$

Step 1

Subtract $3 (x + 2)$ from both sides of the equation.

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

Step 2

Simplify ${(x + 2)}^{2} - 3 (x + 2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x + 2)}^{2}$ as $(x + 2) (x + 2)$ .

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

Step 2.1.2

Expand $(x + 2) (x + 2)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

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

Step 2.1.2.2

Apply the distributive property.

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

Step 2.1.2.3

Apply the distributive property.

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

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

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

Step 2.1.3.1.2

Move $2$ to the left of $x$ .

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

Step 2.1.3.1.3

Multiply $2$ by $2$ .

$x^{2} + 2 x + 2 x + 4 - 3 (x + 2) = 0$

Step 2.1.3.2

Add $2 x$ and $2 x$ .

$x^{2} + 4 x + 4 - 3 (x + 2) = 0$

Step 2.1.4

Apply the distributive property.

$x^{2} + 4 x + 4 - 3 x - 3 \cdot 2 = 0$

Step 2.1.5

Multiply $- 3$ by $2$ .

$x^{2} + 4 x + 4 - 3 x - 6 = 0$

Step 2.2

Subtract $3 x$ from $4 x$ .

$x^{2} + x + 4 - 6 = 0$

Step 2.3

Subtract $6$ from $4$ .

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

Step 3

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

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

Step 4

The standard form is $x^{2} + x - 2$ .

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

Step 5