Evaluate
\left(2n-1\right)^{2}
Expand
4n^{2}-4n+1
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4\left(n^{2}-4n+4\right)+9+12\left(n-2\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(n-2\right)^{2}.
4n^{2}-16n+16+9+12\left(n-2\right)
Use the distributive property to multiply 4 by n^{2}-4n+4.
4n^{2}-16n+25+12\left(n-2\right)
Add 16 and 9 to get 25.
4n^{2}-16n+25+12n-24
Use the distributive property to multiply 12 by n-2.
4n^{2}-4n+25-24
Combine -16n and 12n to get -4n.
4n^{2}-4n+1
Subtract 24 from 25 to get 1.
4\left(n^{2}-4n+4\right)+9+12\left(n-2\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(n-2\right)^{2}.
4n^{2}-16n+16+9+12\left(n-2\right)
Use the distributive property to multiply 4 by n^{2}-4n+4.
4n^{2}-16n+25+12\left(n-2\right)
Add 16 and 9 to get 25.
4n^{2}-16n+25+12n-24
Use the distributive property to multiply 12 by n-2.
4n^{2}-4n+25-24
Combine -16n and 12n to get -4n.
4n^{2}-4n+1
Subtract 24 from 25 to get 1.
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
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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}