# Math Help - How did this happen?

1. ## How did this happen?

This solution comes from a differential calculus book. It seems to be on the simplifying stage already since it involves algebra. I'm wondering how it goes that way. Hopefully someone can explain this to me. Thanks!

2. Originally Posted by stills
This solution comes from a differential calculus book. It seems to be on the simplifying stage already since it involves algebra. I'm wondering how it goes that way. Hopefully someone can explain this to me. Thanks!

$x(x+1)^2$ is a common factor of both the terms.

Try viewing the term as:

$3(a^2)(b^2)+2ab^3$

this can be expressed as:

$ab^2 [ 3a + 2b]$

where:

$a= x$ and $b = x+1$

3. oops,
forget to notice the common factor.
thanks bro
I would like to add another question,
what if, of different exponent?
like this one:

X^4 (x^2-a^2)^-1/2 + 3x^2 (x^2-a^2)^1/2

4. Originally Posted by stills
oops,
forget to notice the common factor.
thanks bro
I would like to add another question,
what if, of different exponent?
like this one:

X^4 (x^2-a^2)^-1/2 + 3x^2 (x^2-a^2)^1/2
that would be:

$\frac{x^4}{\sqrt{(x^2-a^2)}} + 3x^2 \sqrt{(x^2-a^2)}$

Can you simplify this?

5. Originally Posted by stills
This solution comes from a differential calculus book. It seems to be on the simplifying stage already since it involves algebra. I'm wondering how it goes that way. Hopefully someone can explain this to me. Thanks!

It has been factorised by taking out the common factor of $x(x + 1)^2$.