Evaluate
\left(x+\sqrt{2}\right)^{2}
Expand
x^{2}+2\sqrt{2}x+2
Graph
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\left(-x\right)^{2}-2\left(-x\right)\sqrt{2}+\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-x-\sqrt{2}\right)^{2}.
x^{2}-2\left(-x\right)\sqrt{2}+\left(\sqrt{2}\right)^{2}
Calculate -x to the power of 2 and get x^{2}.
x^{2}+2x\sqrt{2}+\left(\sqrt{2}\right)^{2}
Multiply -2 and -1 to get 2.
x^{2}+2x\sqrt{2}+2
The square of \sqrt{2} is 2.
\left(-x\right)^{2}-2\left(-x\right)\sqrt{2}+\left(\sqrt{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-x-\sqrt{2}\right)^{2}.
x^{2}-2\left(-x\right)\sqrt{2}+\left(\sqrt{2}\right)^{2}
Calculate -x to the power of 2 and get x^{2}.
x^{2}+2x\sqrt{2}+\left(\sqrt{2}\right)^{2}
Multiply -2 and -1 to get 2.
x^{2}+2x\sqrt{2}+2
The square of \sqrt{2} is 2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}