Algebra Examples

$p x^{2} + q x + r = (x + 2) (x + 2)$

Step 1

Simplify $(x + 2) (x + 2)$ .

Tap for more steps...

Step 1.1

Rewrite.

$p x^{2} + q x + r = 0 + 0 + (x + 2) (x + 2)$

Step 1.2

Simplify by adding zeros.

$p x^{2} + q x + r = (x + 2) (x + 2)$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$p x^{2} + q x + r = x (x + 2) + 2 (x + 2)$

Step 1.3.2

Apply the distributive property.

$p x^{2} + q x + r = x \cdot x + x \cdot 2 + 2 (x + 2)$

Step 1.3.3

Apply the distributive property.

$p x^{2} + q x + r = x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2$

Step 1.4

Simplify and combine like terms.

Tap for more steps...

Step 1.4.1

Simplify each term.

Tap for more steps...

Step 1.4.1.1

Multiply $x$ by $x$ .

$p x^{2} + q x + r = x^{2} + x \cdot 2 + 2 x + 2 \cdot 2$

Step 1.4.1.2

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

$p x^{2} + q x + r = x^{2} + 2 \cdot x + 2 x + 2 \cdot 2$

Step 1.4.1.3

Multiply $2$ by $2$ .

$p x^{2} + q x + r = x^{2} + 2 x + 2 x + 4$

Step 1.4.2

Add $2 x$ and $2 x$ .

$p x^{2} + q x + r = x^{2} + 4 x + 4$

Step 2

Move all terms not containing $q$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $p x^{2}$ from both sides of the equation.

$q x + r = x^{2} + 4 x + 4 - p x^{2}$

Step 2.2

Subtract $r$ from both sides of the equation.

$q x = x^{2} + 4 x + 4 - p x^{2} - r$

Step 3

Divide each term in $q x = x^{2} + 4 x + 4 - p x^{2} - r$ by $x$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $q x = x^{2} + 4 x + 4 - p x^{2} - r$ by $x$ .

$\frac{q x}{x} = \frac{x^{2}}{x} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{q x}{x} = \frac{x^{2}}{x} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.2.1.2

Divide $q$ by $1$ .

$q = \frac{x^{2}}{x} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Cancel the common factor of $x^{2}$ and $x$ .

Tap for more steps...

Step 3.3.1.1.1

Factor $x$ out of $x^{2}$ .

$q = \frac{x \cdot x}{x} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.1.2.1

Raise $x$ to the power of $1$ .

$q = \frac{x \cdot x}{x^{1}} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.1.2.2

Factor $x$ out of $x^{1}$ .

$q = \frac{x \cdot x}{x \cdot 1} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.1.2.3

Cancel the common factor.

$q = \frac{x \cdot x}{x \cdot 1} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.1.2.4

Rewrite the expression.

$q = \frac{x}{1} + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.1.2.5

Divide $x$ by $1$ .

$q = x + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.3.1.2.1

Cancel the common factor.

$q = x + \frac{4 x}{x} + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.2.2

Divide $4$ by $1$ .

$q = x + 4 + \frac{4}{x} + \frac{- p x^{2}}{x} + \frac{- r}{x}$

Step 3.3.1.3

Cancel the common factor of $x^{2}$ and $x$ .

Tap for more steps...

Step 3.3.1.3.1

Factor $x$ out of $- p x^{2}$ .

$q = x + 4 + \frac{4}{x} + \frac{x (- p x)}{x} + \frac{- r}{x}$

Step 3.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.3.2.1

Raise $x$ to the power of $1$ .

$q = x + 4 + \frac{4}{x} + \frac{x (- p x)}{x^{1}} + \frac{- r}{x}$

Step 3.3.1.3.2.2

Factor $x$ out of $x^{1}$ .

$q = x + 4 + \frac{4}{x} + \frac{x (- p x)}{x \cdot 1} + \frac{- r}{x}$

Step 3.3.1.3.2.3

Cancel the common factor.

$q = x + 4 + \frac{4}{x} + \frac{x (- p x)}{x \cdot 1} + \frac{- r}{x}$

Step 3.3.1.3.2.4

Rewrite the expression.

$q = x + 4 + \frac{4}{x} + \frac{- p x}{1} + \frac{- r}{x}$

Step 3.3.1.3.2.5

Divide $- p x$ by $1$ .

$q = x + 4 + \frac{4}{x} - p x + \frac{- r}{x}$

Step 3.3.1.4

Move the negative in front of the fraction.

$q = x + 4 + \frac{4}{x} - p x - \frac{r}{x}$