Evaluate
-\frac{\left(y+5\right)^{2}}{25}+x^{2}
Expand
-\frac{y^{2}}{25}+x^{2}-\frac{2y}{5}-1
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\left(\frac{5\left(x+1\right)}{5}+\frac{y}{5}\right)\left(x-\frac{y}{5}-1\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x+1 times \frac{5}{5}.
\frac{5\left(x+1\right)+y}{5}\left(x-\frac{y}{5}-1\right)
Since \frac{5\left(x+1\right)}{5} and \frac{y}{5} have the same denominator, add them by adding their numerators.
\frac{5x+5+y}{5}\left(x-\frac{y}{5}-1\right)
Do the multiplications in 5\left(x+1\right)+y.
\frac{5x+5+y}{5}\left(\frac{5\left(x-1\right)}{5}-\frac{y}{5}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x-1 times \frac{5}{5}.
\frac{5x+5+y}{5}\times \frac{5\left(x-1\right)-y}{5}
Since \frac{5\left(x-1\right)}{5} and \frac{y}{5} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+5+y}{5}\times \frac{5x-5-y}{5}
Do the multiplications in 5\left(x-1\right)-y.
\frac{\left(5x+5+y\right)\left(5x-5-y\right)}{5\times 5}
Multiply \frac{5x+5+y}{5} times \frac{5x-5-y}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(5x+5+y\right)\left(5x-5-y\right)}{25}
Multiply 5 and 5 to get 25.
\frac{25x^{2}-25x-5xy+25x-25-5y+5yx-5y-y^{2}}{25}
Apply the distributive property by multiplying each term of 5x+5+y by each term of 5x-5-y.
\frac{25x^{2}-5xy-25-5y+5yx-5y-y^{2}}{25}
Combine -25x and 25x to get 0.
\frac{25x^{2}-25-5y-5y-y^{2}}{25}
Combine -5xy and 5yx to get 0.
\frac{25x^{2}-25-10y-y^{2}}{25}
Combine -5y and -5y to get -10y.
\left(\frac{5\left(x+1\right)}{5}+\frac{y}{5}\right)\left(x-\frac{y}{5}-1\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x+1 times \frac{5}{5}.
\frac{5\left(x+1\right)+y}{5}\left(x-\frac{y}{5}-1\right)
Since \frac{5\left(x+1\right)}{5} and \frac{y}{5} have the same denominator, add them by adding their numerators.
\frac{5x+5+y}{5}\left(x-\frac{y}{5}-1\right)
Do the multiplications in 5\left(x+1\right)+y.
\frac{5x+5+y}{5}\left(\frac{5\left(x-1\right)}{5}-\frac{y}{5}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x-1 times \frac{5}{5}.
\frac{5x+5+y}{5}\times \frac{5\left(x-1\right)-y}{5}
Since \frac{5\left(x-1\right)}{5} and \frac{y}{5} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+5+y}{5}\times \frac{5x-5-y}{5}
Do the multiplications in 5\left(x-1\right)-y.
\frac{\left(5x+5+y\right)\left(5x-5-y\right)}{5\times 5}
Multiply \frac{5x+5+y}{5} times \frac{5x-5-y}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(5x+5+y\right)\left(5x-5-y\right)}{25}
Multiply 5 and 5 to get 25.
\frac{25x^{2}-25x-5xy+25x-25-5y+5yx-5y-y^{2}}{25}
Apply the distributive property by multiplying each term of 5x+5+y by each term of 5x-5-y.
\frac{25x^{2}-5xy-25-5y+5yx-5y-y^{2}}{25}
Combine -25x and 25x to get 0.
\frac{25x^{2}-25-5y-5y-y^{2}}{25}
Combine -5xy and 5yx to get 0.
\frac{25x^{2}-25-10y-y^{2}}{25}
Combine -5y and -5y to get -10y.
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}