Evaluate
\frac{-1302t^{2}+3168t-1728}{25}
Expand
\frac{-1302t^{2}+3168t-1728}{25}
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6t^{2}-\frac{\left(44t-48\right)\left(132t-144\right)}{5\times 20}
Multiply \frac{44t-48}{5} times \frac{132t-144}{20} by multiplying numerator times numerator and denominator times denominator.
6t^{2}-\frac{\left(44t-48\right)\left(132t-144\right)}{100}
Multiply 5 and 20 to get 100.
\frac{100\times 6t^{2}}{100}-\frac{\left(44t-48\right)\left(132t-144\right)}{100}
To add or subtract expressions, expand them to make their denominators the same. Multiply 6t^{2} times \frac{100}{100}.
\frac{100\times 6t^{2}-\left(44t-48\right)\left(132t-144\right)}{100}
Since \frac{100\times 6t^{2}}{100} and \frac{\left(44t-48\right)\left(132t-144\right)}{100} have the same denominator, subtract them by subtracting their numerators.
\frac{600t^{2}-5808t^{2}+6336t+6336t-6912}{100}
Do the multiplications in 100\times 6t^{2}-\left(44t-48\right)\left(132t-144\right).
\frac{-5208t^{2}+12672t-6912}{100}
Combine like terms in 600t^{2}-5808t^{2}+6336t+6336t-6912.
6t^{2}-\frac{\left(44t-48\right)\left(132t-144\right)}{5\times 20}
Multiply \frac{44t-48}{5} times \frac{132t-144}{20} by multiplying numerator times numerator and denominator times denominator.
6t^{2}-\frac{\left(44t-48\right)\left(132t-144\right)}{100}
Multiply 5 and 20 to get 100.
\frac{100\times 6t^{2}}{100}-\frac{\left(44t-48\right)\left(132t-144\right)}{100}
To add or subtract expressions, expand them to make their denominators the same. Multiply 6t^{2} times \frac{100}{100}.
\frac{100\times 6t^{2}-\left(44t-48\right)\left(132t-144\right)}{100}
Since \frac{100\times 6t^{2}}{100} and \frac{\left(44t-48\right)\left(132t-144\right)}{100} have the same denominator, subtract them by subtracting their numerators.
\frac{600t^{2}-5808t^{2}+6336t+6336t-6912}{100}
Do the multiplications in 100\times 6t^{2}-\left(44t-48\right)\left(132t-144\right).
\frac{-5208t^{2}+12672t-6912}{100}
Combine like terms in 600t^{2}-5808t^{2}+6336t+6336t-6912.
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}