Evaluate
\frac{-m^{2}+14m-29}{5}
Expand
\frac{-m^{2}+14m-29}{5}
Share
Copied to clipboard
-\frac{1}{5}\left(m^{2}-4m+4\right)+2m-5
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-2\right)^{2}.
-\frac{1}{5}m^{2}+\frac{4}{5}m-\frac{4}{5}+2m-5
Use the distributive property to multiply -\frac{1}{5} by m^{2}-4m+4.
-\frac{1}{5}m^{2}+\frac{14}{5}m-\frac{4}{5}-5
Combine \frac{4}{5}m and 2m to get \frac{14}{5}m.
-\frac{1}{5}m^{2}+\frac{14}{5}m-\frac{29}{5}
Subtract 5 from -\frac{4}{5} to get -\frac{29}{5}.
-\frac{1}{5}\left(m^{2}-4m+4\right)+2m-5
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-2\right)^{2}.
-\frac{1}{5}m^{2}+\frac{4}{5}m-\frac{4}{5}+2m-5
Use the distributive property to multiply -\frac{1}{5} by m^{2}-4m+4.
-\frac{1}{5}m^{2}+\frac{14}{5}m-\frac{4}{5}-5
Combine \frac{4}{5}m and 2m to get \frac{14}{5}m.
-\frac{1}{5}m^{2}+\frac{14}{5}m-\frac{29}{5}
Subtract 5 from -\frac{4}{5} to get -\frac{29}{5}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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}