Evaluate
\frac{x^{2}}{4}-9y^{2}
Expand
\frac{x^{2}}{4}-9y^{2}
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\left(-\frac{1}{2}x\right)^{2}-\left(3y\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\left(-\frac{1}{2}\right)^{2}x^{2}-\left(3y\right)^{2}
Expand \left(-\frac{1}{2}x\right)^{2}.
\frac{1}{4}x^{2}-\left(3y\right)^{2}
Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.
\frac{1}{4}x^{2}-3^{2}y^{2}
Expand \left(3y\right)^{2}.
\frac{1}{4}x^{2}-9y^{2}
Calculate 3 to the power of 2 and get 9.
\left(-\frac{1}{2}x\right)^{2}-\left(3y\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\left(-\frac{1}{2}\right)^{2}x^{2}-\left(3y\right)^{2}
Expand \left(-\frac{1}{2}x\right)^{2}.
\frac{1}{4}x^{2}-\left(3y\right)^{2}
Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.
\frac{1}{4}x^{2}-3^{2}y^{2}
Expand \left(3y\right)^{2}.
\frac{1}{4}x^{2}-9y^{2}
Calculate 3 to the power of 2 and get 9.
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}