Solve c_6^4-3^2*1

$$c _ { 6 } ^ { 4 } - 3 ^ { 2 } \cdot 1$$

Evaluate

$$c_{6}^{4}-9$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$c_{6}^{4}-9\times 1$$

Multiply 9 and 1 to get 9.

$$c_{6}^{4}-9$$

Factor

$$\left(c_{6}^{2}-3\right)\left(c_{6}^{2}+3\right)$$

Solution Steps

Rewrite c_{6}^{4}-9 as \left(c_{6}^{2}\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right). The following polynomials are not factored since they do not have any rational roots: c_{6}^{2}-3,c_{6}^{2}+3.

$$\left(c_{6}^{2}-3\right)\left(c_{6}^{2}+3\right)$$