Evaluate
\frac{\left(x+2y\right)^{2}}{4}
Expand
xy+\frac{x^{2}}{4}+y^{2}
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\frac{x^{2}}{4}+yx+y^{2}
Use the distributive property to multiply y by x+y.
\frac{x^{2}}{4}+\frac{4\left(yx+y^{2}\right)}{4}
To add or subtract expressions, expand them to make their denominators the same. Multiply yx+y^{2} times \frac{4}{4}.
\frac{x^{2}+4\left(yx+y^{2}\right)}{4}
Since \frac{x^{2}}{4} and \frac{4\left(yx+y^{2}\right)}{4} have the same denominator, add them by adding their numerators.
\frac{x^{2}+4yx+4y^{2}}{4}
Do the multiplications in x^{2}+4\left(yx+y^{2}\right).
\frac{x^{2}}{4}+yx+y^{2}
Use the distributive property to multiply y by x+y.
\frac{x^{2}}{4}+\frac{4\left(yx+y^{2}\right)}{4}
To add or subtract expressions, expand them to make their denominators the same. Multiply yx+y^{2} times \frac{4}{4}.
\frac{x^{2}+4\left(yx+y^{2}\right)}{4}
Since \frac{x^{2}}{4} and \frac{4\left(yx+y^{2}\right)}{4} have the same denominator, add them by adding their numerators.
\frac{x^{2}+4yx+4y^{2}}{4}
Do the multiplications in x^{2}+4\left(yx+y^{2}\right).
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}