To solve this problem you must apply the proccedure shown below:
1- Solve the substraction in the parenthesis and square it:
[tex]\frac{1}{3}+6(\frac{1}{2})^2\\\frac{1}{3}+6(\frac{1}{4})[/tex]
2- Apply the distributive property and solve the addition:
[tex]\frac{1}{3}+\frac{6}{4}\=\frac{11}{6}[/tex]
The answer is: [tex]\frac{11}{6}[/tex]
[tex]\frac{1}{3} +6(\frac{2}{3} - \frac{1}{6})^2[/tex]
first we simplify the parenthesis
To simplify the fractions inside the parenthesis , we make the denominators same
[tex]\frac{1}{3} +6(\frac{2*2}{3*2} - \frac{1}{6})^2[/tex]
[tex]\frac{1}{3} +6(\frac{4}{6} - \frac{1}{6})^2[/tex]
[tex]\frac{1}{3} +6(\frac{3}{6})^2[/tex]
Simplify the fraction 3/6
[tex]\frac{1}{3} +6(\frac{1}{2})^2[/tex]
Now we square 1/2
[tex]\frac{1}{3} +6(\frac{1}{4})[/tex]
Multiply 6 inside the parenthesis
[tex]\frac{1}{3} +\frac{6}{4}[/tex]
[tex]\frac{1}{3} +\frac{3}{2}[/tex]
Now make the denominators same to add fractions
[tex]\frac{1*2}{3*2} +\frac{3*3}{2*3}[/tex]
[tex]\frac{2}{6} +\frac{9}{6}[/tex]
[tex]\frac{11}{6}[/tex]
