### Home > PC3 > Chapter 11 > Lesson 11.1.4 > Problem11-69

11-69.

Complete the parts below to completely factor $x^4 + 2x^2 + 81$.

1. To make a perfect square, what does the middle term need to be (instead of $2x^{2}$)?

$x^{4} + \text{___} + 81 = (x^2 + 9)^2$

2. Explain how $x^{4} + 18x^{2} + 81 − 16x^{2}$ is equivalent to the original expression.

What term was added and subtracted (for a total of $0$) to the original expression?

3. Factor $x^{4} + 18x^{2} + 81$.

4. Factor $u^{2} − 16x^{2}$.

This is a difference of squares.

5. Let $u = x^{2} + 9$ and use your answers to parts (a) through (d) to factor the original expression completely.