Evaluate
27
Factor
3^{3}
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\left(\sqrt{19}\right)^{2}-1^{2}+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
Consider \left(\sqrt{19}+1\right)\left(\sqrt{19}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
19-1^{2}+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
The square of \sqrt{19} is 19.
19-1+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
Calculate 1 to the power of 2 and get 1.
18+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
Subtract 1 from 19 to get 18.
18+\sqrt{10}-1+\left(\sqrt{10}\right)^{2}-\sqrt{10}
Apply the distributive property by multiplying each term of 1+\sqrt{10} by each term of \sqrt{10}-1.
18+\sqrt{10}-1+10-\sqrt{10}
The square of \sqrt{10} is 10.
18+\sqrt{10}+9-\sqrt{10}
Add -1 and 10 to get 9.
18+9
Combine \sqrt{10} and -\sqrt{10} to get 0.
27
Add 18 and 9 to get 27.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}