Solve 4m^6-32m^5+28m^4

$$4 m ^ { 6 } - 32 m ^ { 5 } + 28 m ^ { 4 }$$

Factor

$$4\left(m-7\right)\left(m-1\right)m^{4}$$

Solution Steps

Factor out 4.

$$4\left(m^{6}-8m^{5}+7m^{4}\right)$$

Consider m^{6}-8m^{5}+7m^{4}. Factor out m^{4}.

$$m^{4}\left(m^{2}-8m+7\right)$$

Consider m^{2}-8m+7. Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm+7. To find a and b, set up a system to be solved.

$$a+b=-8 ab=1\times 7=7$$

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

$$a=-7 b=-1$$

Rewrite m^{2}-8m+7 as \left(m^{2}-7m\right)+\left(-m+7\right).

$$\left(m^{2}-7m\right)+\left(-m+7\right)$$

Factor out m in the first and -1 in the second group.

$$m\left(m-7\right)-\left(m-7\right)$$

Factor out common term m-7 by using distributive property.

$$\left(m-7\right)\left(m-1\right)$$

Rewrite the complete factored expression.

$$4m^{4}\left(m-7\right)\left(m-1\right)$$

Evaluate

$$4\left(m-7\right)\left(m-1\right)m^{4}$$