# How do you factor a^4-2a^2-48?

##### 1 Answer
Jun 30, 2018

$\left({a}^{2} - 8\right) \left({a}^{2} + 6\right)$

#### Explanation:

Re-write the equation as:

$\left(\left({a}^{4}\right) - \left(2 {a}^{2}\right)\right) - 48$

Trying to factor by splitting middle term:

Step 1: Find two factors of $- 48$ whose sum equals the coefficient of the middle term, which is $- 2$.

$- 8 + 6 = - 2$

and

$- 8 \times 6 = - 48$

Step 2: Rewrite the polynomial splitting the middle term using the two factors found in step 1 above, $- 8$ and $6$

${a}^{4} - 8 {a}^{2} + 6 {a}^{2} - 48$

Step 3: Pull out the common factor

${a}^{2} \left({a}^{2} - 8\right) + 6 \left({a}^{2} - 8\right)$

$\left({a}^{2} - 8\right) \left({a}^{2} + 6\right)$ ----> desired factors!