Solve 9-m^4

$$9 - m ^ { 4 }$$

Factor

$$\left(-m^{2}-3\right)\left(m^{2}-3\right)$$

Solution Steps

Rewrite 9-m^{4} as 3^{2}-\left(-m^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3+m^{2}\right)\left(3-m^{2}\right)$$

Reorder the terms. The following polynomials are not factored since they do not have any rational roots: -m^{2}+3,m^{2}+3.

$$\left(m^{2}+3\right)\left(-m^{2}+3\right)$$

Evaluate

$$9-m^{4}$$