Evaluate
4+12x-11x^{2}
Expand
4+12x-11x^{2}
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\left(-2x-4\right)\left(x-2\right)-\left(3x-2\right)^{2}
Use the distributive property to multiply -2 by x+2.
-2x^{2}+8-\left(3x-2\right)^{2}
Use the distributive property to multiply -2x-4 by x-2 and combine like terms.
-2x^{2}+8-\left(9x^{2}-12x+4\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.
-2x^{2}+8-9x^{2}+12x-4
To find the opposite of 9x^{2}-12x+4, find the opposite of each term.
-11x^{2}+8+12x-4
Combine -2x^{2} and -9x^{2} to get -11x^{2}.
-11x^{2}+4+12x
Subtract 4 from 8 to get 4.
\left(-2x-4\right)\left(x-2\right)-\left(3x-2\right)^{2}
Use the distributive property to multiply -2 by x+2.
-2x^{2}+8-\left(3x-2\right)^{2}
Use the distributive property to multiply -2x-4 by x-2 and combine like terms.
-2x^{2}+8-\left(9x^{2}-12x+4\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.
-2x^{2}+8-9x^{2}+12x-4
To find the opposite of 9x^{2}-12x+4, find the opposite of each term.
-11x^{2}+8+12x-4
Combine -2x^{2} and -9x^{2} to get -11x^{2}.
-11x^{2}+4+12x
Subtract 4 from 8 to get 4.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}