Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.2

Raise $- 1$ to the power of $2$ .

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

Step 1.3

Multiply $\frac{3^{2}}{2^{2}}$ by $1$ .

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

Step 1.4

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

$\frac{9}{2^{2}} + 2 (- \frac{3}{2})$

Step 1.5

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

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

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 1.6.2

Cancel the common factor.

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

Step 1.6.3

Rewrite the expression.

$\frac{9}{4} - 3$

Step 2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{4} - 3 \cdot \frac{4}{4}$

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

$\frac{9 - 3 \cdot 4}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $4$ .

$\frac{9 - 12}{4}$

Step 5.2

Subtract $12$ from $9$ .

$\frac{- 3}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{4}$

Decimal Form:

$- 0.75$