[MOVED] Factoring expression: (3x - 2)^-4 (x + 3) + ....

[kC_Lee]

How would you factor (3x - 2)^-4 (x + 3) + (x + 3)^2 (3x - 2)^-3

 

[stapel]

Take out the common factors of (3x - 2)^-3(x + 3), and then simplify what's left.

Eliz.

 

[soroban]

Re: Factoring expression

Hello, kC_Lee!

This is not a Calculus problem . . .
$\displaystyle \;\;$but I bet it came from the Product Rule.

How would you factor: \(\displaystyle \,(x\,+\,3)(3x\,-\,2)^{-4}\:+\x\,+\,3)^2 (3x\,-\,2)^{-3}\)

We have: $\displaystyle \,ab^{-4}\,+\,a^2b^{-3}$ . . . which factors: $\displaystyle \,ab^{-4}(1\,+\,ab)$


Hence: \(\displaystyle \,(x\,+\,3)(3x\,-\,2)^{-4}\:+\x\,+\,3)^2 (3x\,-\,2)^{-3} \;= \;(x\,+\,3)(3x\,-\,2)^{-4}\left[1\,+\,(x\,+\,3)(3x\,-\,2)\right]\)

. . $\displaystyle = \;(x\,+\,3)(3x\,-\,2)^{-4}\left[1\,+\,3x^2\,+\,7x\,-\,6\right] \;= \;(x\,+\,3)(3x\,-\,2)(3x^2\,+\,7x\,-\,5)$

 

[kC_Lee]

oh I get it now. thanks for the help!