Evaluate
9+12z-8z^{2}
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9+12z-8z^{2}
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4z^{2}+12z+9+2z\left(-5z-z\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2z+3\right)^{2}.
4z^{2}+12z+9+2z\left(-6\right)z
Combine -5z and -z to get -6z.
4z^{2}+12z+9-12zz
Multiply 2 and -6 to get -12.
4z^{2}+12z+9-12z^{2}
Multiply z and z to get z^{2}.
-8z^{2}+12z+9
Combine 4z^{2} and -12z^{2} to get -8z^{2}.
4z^{2}+12z+9+2z\left(-5z-z\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2z+3\right)^{2}.
4z^{2}+12z+9+2z\left(-6\right)z
Combine -5z and -z to get -6z.
4z^{2}+12z+9-12zz
Multiply 2 and -6 to get -12.
4z^{2}+12z+9-12z^{2}
Multiply z and z to get z^{2}.
-8z^{2}+12z+9
Combine 4z^{2} and -12z^{2} to get -8z^{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
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