Simplify 1/4+4(1/2-3/4)^2

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

Step 1

Simplify each term.

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

$\frac{1}{4} + 4 {(\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{4})}^{2}$

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

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

$\frac{1}{4} + 4 {(\frac{2}{2 \cdot 2} - \frac{3}{4})}^{2}$

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $2$ .

$\frac{1}{4} + 4 {(\frac{- 1}{4})}^{2}$

Move the negative in front of the fraction.

$\frac{1}{4} + 4 {(- \frac{1}{4})}^{2}$

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

Apply the product rule to $- \frac{1}{4}$ .

$\frac{1}{4} + 4 ({(- 1)}^{2} {(\frac{1}{4})}^{2})$

Apply the product rule to $\frac{1}{4}$ .

$\frac{1}{4} + 4 ({(- 1)}^{2} \frac{1^{2}}{4^{2}})$

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

$\frac{1}{4} + 4 (1 \frac{1^{2}}{4^{2}})$

Multiply $\frac{1^{2}}{4^{2}}$ by $1$ .

$\frac{1}{4} + 4 \frac{1^{2}}{4^{2}}$

One to any power is one.

$\frac{1}{4} + 4 \frac{1}{4^{2}}$

Raise $4$ to the power of $2$ .

$\frac{1}{4} + 4 (\frac{1}{16})$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$\frac{1}{4} + 4 \frac{1}{4 (4)}$

Cancel the common factor.

$\frac{1}{4} + 4 \frac{1}{4 \cdot 4}$

Rewrite the expression.

$\frac{1}{4} + \frac{1}{4}$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$\frac{1 + 1}{4}$

Add $1$ and $1$ .

$\frac{2}{4}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

Simplify 1/4+4(1/2-3/4)^2

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