Evaluate
\left(2x-1\right)^{2}
Expand
4x^{2}-4x+1
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4\left(x^{2}+2x+1\right)-12\left(x+1\right)+9
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
4x^{2}+8x+4-12\left(x+1\right)+9
Use the distributive property to multiply 4 by x^{2}+2x+1.
4x^{2}+8x+4-12x-12+9
Use the distributive property to multiply -12 by x+1.
4x^{2}-4x+4-12+9
Combine 8x and -12x to get -4x.
4x^{2}-4x-8+9
Subtract 12 from 4 to get -8.
4x^{2}-4x+1
Add -8 and 9 to get 1.
4\left(x^{2}+2x+1\right)-12\left(x+1\right)+9
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
4x^{2}+8x+4-12\left(x+1\right)+9
Use the distributive property to multiply 4 by x^{2}+2x+1.
4x^{2}+8x+4-12x-12+9
Use the distributive property to multiply -12 by x+1.
4x^{2}-4x+4-12+9
Combine 8x and -12x to get -4x.
4x^{2}-4x-8+9
Subtract 12 from 4 to get -8.
4x^{2}-4x+1
Add -8 and 9 to get 1.
Examples
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y = 3x + 4
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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}