# Factoring and Simplifying

I'm trying to do this problem,

$$(4x + 1)^{15}\cdot\frac{1}{3}(12x - 5)^{-\frac{2}{3}}\cdot 12 + (12x - 5)^{\frac{1}{3}}\cdot15(4x + 1)^{14}\cdot 4$$

I've gotten down to,

$$4(4x+1)^{15}(12x-5)^{-\frac{2}{3}} + 60(12x-5)^{\frac{1}{3}}(4x+1)^{14}$$

I'm really wanting to understand how to finish this problem and the steps necessary from this point. Math isn't my strong suit. If you reply to this, I'd greatly appreciate an explanation/step by step. Thank you!

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Please use latex to format your question, to make it comprehensible. (4x+1)^15(1/3)(12x - 5)^-2/3(12) could mean $(4x + 1)^{\frac{15}{3}}\cdot(12x - 5)^{12\cdot\frac{-2}{3}}$, or $(4x + 1)^15\cdot\frac{1}{3}\cdot(12x - 5)^{-2} / 3 \cdot 12$ or some thing different altogether. –  Lee Yiyuan May 1 '14 at 8:14
(4x+1)^(15)(1/3)(12x-5)^(-2/3)(12) + (12x-5)^(1/3)(15)(4x+1)^(14)(4) ? I don' t know how to convert it into a different format. =\ –  Blake May 1 '14 at 8:32
(4x+1)^15∙(1/3)∙(12x-5)^-(2/3)∙(12)+(12x-5)^(1/3)∙(15)∙(4x+1)^14∙(4) –  Blake May 1 '14 at 8:40
You could write it out on a paper (or microsoft paint) and post it over here, and we'll see what we can do. –  Lee Yiyuan May 1 '14 at 8:42
i590.photobucket.com/albums/ss349/deutonus/mathproblem.png Okay, i wrote it out on paint. Haha –  Blake May 1 '14 at 9:13

Force out the common factor of $(4x + 1)^{14} (12x - 5)^{-\frac{2}{3}}$ to get
$$(4x + 1)^{14} (12x - 5)^{-\frac{2}{3}}\left((4x + 1)\cdot\frac{1}{3}\cdot 12 + (12x - 5)\cdot 15 \cdot 4\right)$$
$$(4x + 1)^{14} (12x - 5)^{-\frac{2}{3}}(736x - 296)$$
You do $\frac{1}{3} = 1 - \frac{2}{3}$ and take out the $\frac{2}{3}$ to leave $1$. –  Lee Yiyuan May 1 '14 at 9:33