Evaluate
\frac{4xy}{5}+\frac{3y^{2}}{16}+\frac{16x^{2}}{25}
Expand
\frac{4xy}{5}+\frac{3y^{2}}{16}+\frac{16x^{2}}{25}
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\left(\frac{4\times 4x}{20}+\frac{5y}{20}\right)\left(\frac{4x}{5}+\frac{3y}{4}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 4 is 20. Multiply \frac{4x}{5} times \frac{4}{4}. Multiply \frac{y}{4} times \frac{5}{5}.
\frac{4\times 4x+5y}{20}\left(\frac{4x}{5}+\frac{3y}{4}\right)
Since \frac{4\times 4x}{20} and \frac{5y}{20} have the same denominator, add them by adding their numerators.
\frac{16x+5y}{20}\left(\frac{4x}{5}+\frac{3y}{4}\right)
Do the multiplications in 4\times 4x+5y.
\frac{16x+5y}{20}\left(\frac{4\times 4x}{20}+\frac{5\times 3y}{20}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 4 is 20. Multiply \frac{4x}{5} times \frac{4}{4}. Multiply \frac{3y}{4} times \frac{5}{5}.
\frac{16x+5y}{20}\times \frac{4\times 4x+5\times 3y}{20}
Since \frac{4\times 4x}{20} and \frac{5\times 3y}{20} have the same denominator, add them by adding their numerators.
\frac{16x+5y}{20}\times \frac{16x+15y}{20}
Do the multiplications in 4\times 4x+5\times 3y.
\frac{\left(16x+5y\right)\left(16x+15y\right)}{20\times 20}
Multiply \frac{16x+5y}{20} times \frac{16x+15y}{20} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(16x+5y\right)\left(16x+15y\right)}{400}
Multiply 20 and 20 to get 400.
\frac{256x^{2}+240xy+80yx+75y^{2}}{400}
Apply the distributive property by multiplying each term of 16x+5y by each term of 16x+15y.
\frac{256x^{2}+320xy+75y^{2}}{400}
Combine 240xy and 80yx to get 320xy.
\left(\frac{4\times 4x}{20}+\frac{5y}{20}\right)\left(\frac{4x}{5}+\frac{3y}{4}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 4 is 20. Multiply \frac{4x}{5} times \frac{4}{4}. Multiply \frac{y}{4} times \frac{5}{5}.
\frac{4\times 4x+5y}{20}\left(\frac{4x}{5}+\frac{3y}{4}\right)
Since \frac{4\times 4x}{20} and \frac{5y}{20} have the same denominator, add them by adding their numerators.
\frac{16x+5y}{20}\left(\frac{4x}{5}+\frac{3y}{4}\right)
Do the multiplications in 4\times 4x+5y.
\frac{16x+5y}{20}\left(\frac{4\times 4x}{20}+\frac{5\times 3y}{20}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 4 is 20. Multiply \frac{4x}{5} times \frac{4}{4}. Multiply \frac{3y}{4} times \frac{5}{5}.
\frac{16x+5y}{20}\times \frac{4\times 4x+5\times 3y}{20}
Since \frac{4\times 4x}{20} and \frac{5\times 3y}{20} have the same denominator, add them by adding their numerators.
\frac{16x+5y}{20}\times \frac{16x+15y}{20}
Do the multiplications in 4\times 4x+5\times 3y.
\frac{\left(16x+5y\right)\left(16x+15y\right)}{20\times 20}
Multiply \frac{16x+5y}{20} times \frac{16x+15y}{20} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(16x+5y\right)\left(16x+15y\right)}{400}
Multiply 20 and 20 to get 400.
\frac{256x^{2}+240xy+80yx+75y^{2}}{400}
Apply the distributive property by multiplying each term of 16x+5y by each term of 16x+15y.
\frac{256x^{2}+320xy+75y^{2}}{400}
Combine 240xy and 80yx to get 320xy.
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}