Evaluate
x^{2}+2y^{2}
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x^{2}+2y^{2}
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x^{2}+4xy+4y^{2}-2y\left(y+2x\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.
x^{2}+4xy+4y^{2}-2y^{2}-4yx
Use the distributive property to multiply -2y by y+2x.
x^{2}+4xy+2y^{2}-4yx
Combine 4y^{2} and -2y^{2} to get 2y^{2}.
x^{2}+2y^{2}
Combine 4xy and -4yx to get 0.
x^{2}+4xy+4y^{2}-2y\left(y+2x\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.
x^{2}+4xy+4y^{2}-2y^{2}-4yx
Use the distributive property to multiply -2y by y+2x.
x^{2}+4xy+2y^{2}-4yx
Combine 4y^{2} and -2y^{2} to get 2y^{2}.
x^{2}+2y^{2}
Combine 4xy and -4yx to get 0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
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Limits
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