Solve 2m^4-4m^2+2

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

Factor

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

Solution Steps

Factor out 2.

$$2\left(m^{4}-2m^{2}+1\right)$$

Consider m^{4}-2m^{2}+1. Find one factor of the form m^{k}+n, where m^{k} divides the monomial with the highest power m^{4} and n divides the constant factor 1. One such factor is m^{2}-1. Factor the polynomial by dividing it by this factor.

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

Consider m^{2}-1. Rewrite m^{2}-1 as m^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression.

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

Evaluate

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