Evaluate
\frac{5t^{2}}{8}-24
Expand
\frac{5t^{2}}{8}-24
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16-\frac{1}{2}\left(8-t\right)\left(\frac{5}{4}t+10\right)
Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.
16+\left(-\frac{1}{2}\times 8-\frac{1}{2}\left(-1\right)t\right)\left(\frac{5}{4}t+10\right)
Use the distributive property to multiply -\frac{1}{2} by 8-t.
16+\left(\frac{-8}{2}-\frac{1}{2}\left(-1\right)t\right)\left(\frac{5}{4}t+10\right)
Express -\frac{1}{2}\times 8 as a single fraction.
16+\left(-4-\frac{1}{2}\left(-1\right)t\right)\left(\frac{5}{4}t+10\right)
Divide -8 by 2 to get -4.
16+\left(-4+\frac{1}{2}t\right)\left(\frac{5}{4}t+10\right)
Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.
16-4\times \frac{5}{4}t-40+\frac{1}{2}t\times \frac{5}{4}t+\frac{1}{2}t\times 10
Apply the distributive property by multiplying each term of -4+\frac{1}{2}t by each term of \frac{5}{4}t+10.
16-4\times \frac{5}{4}t-40+\frac{1}{2}t^{2}\times \frac{5}{4}+\frac{1}{2}t\times 10
Multiply t and t to get t^{2}.
16-5t-40+\frac{1}{2}t^{2}\times \frac{5}{4}+\frac{1}{2}t\times 10
Multiply -4 times \frac{5}{4}.
16-5t-40+\frac{1\times 5}{2\times 4}t^{2}+\frac{1}{2}t\times 10
Multiply \frac{1}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.
16-5t-40+\frac{5}{8}t^{2}+\frac{1}{2}t\times 10
Do the multiplications in the fraction \frac{1\times 5}{2\times 4}.
16-5t-40+\frac{5}{8}t^{2}+\frac{10}{2}t
Multiply \frac{1}{2} and 10 to get \frac{10}{2}.
16-5t-40+\frac{5}{8}t^{2}+5t
Divide 10 by 2 to get 5.
16-40+\frac{5}{8}t^{2}
Combine -5t and 5t to get 0.
-24+\frac{5}{8}t^{2}
Subtract 40 from 16 to get -24.
16-\frac{1}{2}\left(8-t\right)\left(\frac{5}{4}t+10\right)
Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.
16+\left(-\frac{1}{2}\times 8-\frac{1}{2}\left(-1\right)t\right)\left(\frac{5}{4}t+10\right)
Use the distributive property to multiply -\frac{1}{2} by 8-t.
16+\left(\frac{-8}{2}-\frac{1}{2}\left(-1\right)t\right)\left(\frac{5}{4}t+10\right)
Express -\frac{1}{2}\times 8 as a single fraction.
16+\left(-4-\frac{1}{2}\left(-1\right)t\right)\left(\frac{5}{4}t+10\right)
Divide -8 by 2 to get -4.
16+\left(-4+\frac{1}{2}t\right)\left(\frac{5}{4}t+10\right)
Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.
16-4\times \frac{5}{4}t-40+\frac{1}{2}t\times \frac{5}{4}t+\frac{1}{2}t\times 10
Apply the distributive property by multiplying each term of -4+\frac{1}{2}t by each term of \frac{5}{4}t+10.
16-4\times \frac{5}{4}t-40+\frac{1}{2}t^{2}\times \frac{5}{4}+\frac{1}{2}t\times 10
Multiply t and t to get t^{2}.
16-5t-40+\frac{1}{2}t^{2}\times \frac{5}{4}+\frac{1}{2}t\times 10
Multiply -4 times \frac{5}{4}.
16-5t-40+\frac{1\times 5}{2\times 4}t^{2}+\frac{1}{2}t\times 10
Multiply \frac{1}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.
16-5t-40+\frac{5}{8}t^{2}+\frac{1}{2}t\times 10
Do the multiplications in the fraction \frac{1\times 5}{2\times 4}.
16-5t-40+\frac{5}{8}t^{2}+\frac{10}{2}t
Multiply \frac{1}{2} and 10 to get \frac{10}{2}.
16-5t-40+\frac{5}{8}t^{2}+5t
Divide 10 by 2 to get 5.
16-40+\frac{5}{8}t^{2}
Combine -5t and 5t to get 0.
-24+\frac{5}{8}t^{2}
Subtract 40 from 16 to get -24.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}