Evaluate
\frac{\left(2a-3b\right)^{2}}{36}
Expand
-\frac{ab}{3}+\frac{a^{2}}{9}+\frac{b^{2}}{4}
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\left(-\frac{1}{3}a+\frac{1}{2}b\right)^{2}
Use the distributive property to multiply -\frac{1}{6} by 2a-3b.
\frac{1}{9}a^{2}-\frac{1}{3}ab+\frac{1}{4}b^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(-\frac{1}{3}a+\frac{1}{2}b\right)^{2}.
\left(-\frac{1}{3}a+\frac{1}{2}b\right)^{2}
Use the distributive property to multiply -\frac{1}{6} by 2a-3b.
\frac{1}{9}a^{2}-\frac{1}{3}ab+\frac{1}{4}b^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(-\frac{1}{3}a+\frac{1}{2}b\right)^{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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
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