# Algebraic steps to simplify an equation

1. Mar 7, 2010

### JOhnJDC

1. The problem statement, all variables and given/known data
Could someone show me the algebraic steps involved in the following equivalency?

2. Relevant equations

3. The attempt at a solution

EDIT: see attempt below. I eventually answered my own question. Thanks, Mark44.

Last edited: Mar 7, 2010
2. Mar 7, 2010

### Staff: Mentor

$$2(q + \frac{pq}{a})(\frac{-rq}{a^2}) + 2(p + a)$$
$$=2(\frac{-pq^2}{a^2} + \frac{-p^2q^2}{a^3}) + 2(p + a)$$

Get a common denominator for the two terms in the first pair of parentheses, and then combine those two terms.
Can you carry on from there?

3. Mar 7, 2010

### JOhnJDC

Okay, the two terms in parentheses now have a common denominator:

2(a+p) + 2(-apq^2 - p^2q^2)/a^3

This is where I get stuck. I don't know how to factor 2(a+p) out of the numerator 2(-apq^2 - p^2q^2).

Here is my attempt:

2a+2p + (-2apq^2 - 2p^2q^2)/a^3

(2a+2p)[1 + (-pq^2 - pq^2)/a^3]

2(a+p)[1 + (-2pq^2)/a^3]

What am I doing wrong? Why do I end up with -2pq^2/a^3 instead of just pq^2/a^3? Thanks.

EDIT: I got it. I was thinking about the operation in the wrong way. Instead of trying to factor out (a+p), I decided to factor out -pq^2 from 2(-apq^2-p^2q^2)/a^3, which yielded 2[-pq^2(a+p)/a^3]. From there, I could easily factor out 2(a+p) from 2(a+p) + 2(-apq^2 - p^2q^2)/a^3.

Thanks.

Last edited: Mar 7, 2010