Evaluate
1+4x-6x^{2}
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1+4x-6x^{2}
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4x^{2}+4x+1-5x\left(2x+1\right)+2\left(2x+1\right)+x-2
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.
4x^{2}+4x+1-5x\left(2x+1\right)+4x+2+x-2
Use the distributive property to multiply 2 by 2x+1.
4x^{2}+4x+1-5x\left(2x+1\right)+5x+2-2
Combine 4x and x to get 5x.
4x^{2}+4x+1-5x\left(2x+1\right)+5x
Subtract 2 from 2 to get 0.
4x^{2}+4x+1-10x^{2}-5x+5x
Use the distributive property to multiply -5x by 2x+1.
-6x^{2}+4x+1-5x+5x
Combine 4x^{2} and -10x^{2} to get -6x^{2}.
-6x^{2}-x+1+5x
Combine 4x and -5x to get -x.
-6x^{2}+4x+1
Combine -x and 5x to get 4x.
4x^{2}+4x+1-5x\left(2x+1\right)+2\left(2x+1\right)+x-2
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.
4x^{2}+4x+1-5x\left(2x+1\right)+4x+2+x-2
Use the distributive property to multiply 2 by 2x+1.
4x^{2}+4x+1-5x\left(2x+1\right)+5x+2-2
Combine 4x and x to get 5x.
4x^{2}+4x+1-5x\left(2x+1\right)+5x
Subtract 2 from 2 to get 0.
4x^{2}+4x+1-10x^{2}-5x+5x
Use the distributive property to multiply -5x by 2x+1.
-6x^{2}+4x+1-5x+5x
Combine 4x^{2} and -10x^{2} to get -6x^{2}.
-6x^{2}-x+1+5x
Combine 4x and -5x to get -x.
-6x^{2}+4x+1
Combine -x and 5x to get 4x.
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
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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}