Solve {r}{m^2-4m+5}{-2m^2+6m-6}

$$\left. \begin{array} { r } { m ^ { 2 } - 4 m + 5 } \\ { - 2 m ^ { 2 } + 6 m - 6 } \end{array} \right.$$

Evaluate

$$-\left(m-1\right)^{2}$$

Solution Steps

Combine m^{2} and -2m^{2} to get -m^{2}.

$$-m^{2}-4m+5+6m-6$$

Combine -4m and 6m to get 2m.

$$-m^{2}+2m+5-6$$

Subtract 6 from 5 to get -1.

$$-m^{2}+2m-1$$

Factor

$$-\left(m-1\right)^{2}$$

Solution Steps

Multiply and combine like terms.

$$-m^{2}+2m-1$$

Factor the expression by grouping. First, the expression needs to be rewritten as -m^{2}+am+bm-1. To find a and b, set up a system to be solved.

$$a+b=2 ab=-\left(-1\right)=1$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=1 b=1$$

Rewrite -m^{2}+2m-1 as \left(-m^{2}+m\right)+\left(m-1\right).

$$\left(-m^{2}+m\right)+\left(m-1\right)$$

Factor out -m in -m^{2}+m.

$$-m\left(m-1\right)+m-1$$

Factor out common term m-1 by using distributive property.

$$\left(m-1\right)\left(-m+1\right)$$