Algebra Examples

$\frac{1}{2} - 3 {(\frac{1}{2} + 1)}^{2}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{1}{2} - 3 {(\frac{1}{2} + \frac{2}{2})}^{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{2} - 3 {(\frac{1 + 2}{2})}^{2}$

Step 1.3

Add $1$ and $2$ .

$\frac{1}{2} - 3 {(\frac{3}{2})}^{2}$

Step 1.4

Apply the product rule to $\frac{3}{2}$ .

$\frac{1}{2} - 3 \frac{3^{2}}{2^{2}}$

Step 1.5

Raise $3$ to the power of $2$ .

$\frac{1}{2} - 3 \frac{9}{2^{2}}$

Step 1.6

Raise $2$ to the power of $2$ .

$\frac{1}{2} - 3 (\frac{9}{4})$

Step 1.7

Multiply $- 3 (\frac{9}{4})$ .

Tap for more steps...

Step 1.7.1

Combine $- 3$ and $\frac{9}{4}$ .

$\frac{1}{2} + \frac{- 3 \cdot 9}{4}$

Step 1.7.2

Multiply $- 3$ by $9$ .

$\frac{1}{2} + \frac{- 27}{4}$

Step 1.8

Move the negative in front of the fraction.

$\frac{1}{2} - \frac{27}{4}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} \cdot \frac{2}{2} - \frac{27}{4}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{2}{2 \cdot 2} - \frac{27}{4}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{2}{4} - \frac{27}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 - 27}{4}$

Step 5

Subtract $27$ from $2$ .

$\frac{- 25}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{25}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{4}$

Decimal Form:

$- 6.25$

Mixed Number Form:

$- 6 \frac{1}{4}$