Evaluate
\frac{xy}{7}-\frac{15y^{2}}{49}+6x^{2}
Expand
\frac{xy}{7}-\frac{15y^{2}}{49}+6x^{2}
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\left(\frac{7\times 3x}{7}+\frac{5y}{7}\right)\left(2x-\frac{3y}{7}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{7}{7}.
\frac{7\times 3x+5y}{7}\left(2x-\frac{3y}{7}\right)
Since \frac{7\times 3x}{7} and \frac{5y}{7} have the same denominator, add them by adding their numerators.
\frac{21x+5y}{7}\left(2x-\frac{3y}{7}\right)
Do the multiplications in 7\times 3x+5y.
\frac{21x+5y}{7}\left(\frac{7\times 2x}{7}-\frac{3y}{7}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{7}{7}.
\frac{21x+5y}{7}\times \frac{7\times 2x-3y}{7}
Since \frac{7\times 2x}{7} and \frac{3y}{7} have the same denominator, subtract them by subtracting their numerators.
\frac{21x+5y}{7}\times \frac{14x-3y}{7}
Do the multiplications in 7\times 2x-3y.
\frac{\left(21x+5y\right)\left(14x-3y\right)}{7\times 7}
Multiply \frac{21x+5y}{7} times \frac{14x-3y}{7} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(21x+5y\right)\left(14x-3y\right)}{49}
Multiply 7 and 7 to get 49.
\frac{294x^{2}-63xy+70yx-15y^{2}}{49}
Apply the distributive property by multiplying each term of 21x+5y by each term of 14x-3y.
\frac{294x^{2}+7xy-15y^{2}}{49}
Combine -63xy and 70yx to get 7xy.
\left(\frac{7\times 3x}{7}+\frac{5y}{7}\right)\left(2x-\frac{3y}{7}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{7}{7}.
\frac{7\times 3x+5y}{7}\left(2x-\frac{3y}{7}\right)
Since \frac{7\times 3x}{7} and \frac{5y}{7} have the same denominator, add them by adding their numerators.
\frac{21x+5y}{7}\left(2x-\frac{3y}{7}\right)
Do the multiplications in 7\times 3x+5y.
\frac{21x+5y}{7}\left(\frac{7\times 2x}{7}-\frac{3y}{7}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{7}{7}.
\frac{21x+5y}{7}\times \frac{7\times 2x-3y}{7}
Since \frac{7\times 2x}{7} and \frac{3y}{7} have the same denominator, subtract them by subtracting their numerators.
\frac{21x+5y}{7}\times \frac{14x-3y}{7}
Do the multiplications in 7\times 2x-3y.
\frac{\left(21x+5y\right)\left(14x-3y\right)}{7\times 7}
Multiply \frac{21x+5y}{7} times \frac{14x-3y}{7} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(21x+5y\right)\left(14x-3y\right)}{49}
Multiply 7 and 7 to get 49.
\frac{294x^{2}-63xy+70yx-15y^{2}}{49}
Apply the distributive property by multiplying each term of 21x+5y by each term of 14x-3y.
\frac{294x^{2}+7xy-15y^{2}}{49}
Combine -63xy and 70yx to get 7xy.
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}