Evaluate
\frac{x^{2}}{9}-x-\frac{27}{4}
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\frac{x^{2}}{9}-x-\frac{27}{4}
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\frac{1}{3}x\times \frac{1}{3}x+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Apply the distributive property by multiplying each term of \frac{1}{3}x+\frac{3}{2} by each term of \frac{1}{3}x-\frac{9}{2}.
\frac{1}{3}x^{2}\times \frac{1}{3}+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply x and x to get x^{2}.
\frac{1\times 1}{3\times 3}x^{2}+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply \frac{1}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Do the multiplications in the fraction \frac{1\times 1}{3\times 3}.
\frac{1}{9}x^{2}+\frac{1\left(-9\right)}{3\times 2}x+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply \frac{1}{3} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}+\frac{-9}{6}x+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Do the multiplications in the fraction \frac{1\left(-9\right)}{3\times 2}.
\frac{1}{9}x^{2}-\frac{3}{2}x+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.
\frac{1}{9}x^{2}-\frac{3}{2}x+\frac{3\times 1}{2\times 3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}-\frac{3}{2}x+\frac{1}{2}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Cancel out 3 in both numerator and denominator.
\frac{1}{9}x^{2}-x+\frac{3}{2}\left(-\frac{9}{2}\right)
Combine -\frac{3}{2}x and \frac{1}{2}x to get -x.
\frac{1}{9}x^{2}-x+\frac{3\left(-9\right)}{2\times 2}
Multiply \frac{3}{2} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}-x+\frac{-27}{4}
Do the multiplications in the fraction \frac{3\left(-9\right)}{2\times 2}.
\frac{1}{9}x^{2}-x-\frac{27}{4}
Fraction \frac{-27}{4} can be rewritten as -\frac{27}{4} by extracting the negative sign.
\frac{1}{3}x\times \frac{1}{3}x+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Apply the distributive property by multiplying each term of \frac{1}{3}x+\frac{3}{2} by each term of \frac{1}{3}x-\frac{9}{2}.
\frac{1}{3}x^{2}\times \frac{1}{3}+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply x and x to get x^{2}.
\frac{1\times 1}{3\times 3}x^{2}+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply \frac{1}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}+\frac{1}{3}x\left(-\frac{9}{2}\right)+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Do the multiplications in the fraction \frac{1\times 1}{3\times 3}.
\frac{1}{9}x^{2}+\frac{1\left(-9\right)}{3\times 2}x+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply \frac{1}{3} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}+\frac{-9}{6}x+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Do the multiplications in the fraction \frac{1\left(-9\right)}{3\times 2}.
\frac{1}{9}x^{2}-\frac{3}{2}x+\frac{3}{2}\times \frac{1}{3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.
\frac{1}{9}x^{2}-\frac{3}{2}x+\frac{3\times 1}{2\times 3}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}-\frac{3}{2}x+\frac{1}{2}x+\frac{3}{2}\left(-\frac{9}{2}\right)
Cancel out 3 in both numerator and denominator.
\frac{1}{9}x^{2}-x+\frac{3}{2}\left(-\frac{9}{2}\right)
Combine -\frac{3}{2}x and \frac{1}{2}x to get -x.
\frac{1}{9}x^{2}-x+\frac{3\left(-9\right)}{2\times 2}
Multiply \frac{3}{2} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{9}x^{2}-x+\frac{-27}{4}
Do the multiplications in the fraction \frac{3\left(-9\right)}{2\times 2}.
\frac{1}{9}x^{2}-x-\frac{27}{4}
Fraction \frac{-27}{4} can be rewritten as -\frac{27}{4} by extracting the negative sign.
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Differentiation
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Integration
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Limits
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