Solve 9m^4-900

$$9 m ^ { 4 } - 900$$

Factor

$$9\left(m^{2}-10\right)\left(m^{2}+10\right)$$

Solution Steps

Factor out 9.

$$9\left(m^{4}-100\right)$$

Consider m^{4}-100. Rewrite m^{4}-100 as \left(m^{2}\right)^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m^{2}-10\right)\left(m^{2}+10\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: m^{2}-10,m^{2}+10.

$$9\left(m^{2}-10\right)\left(m^{2}+10\right)$$

Evaluate

$$9\left(m^{4}-100\right)$$