Question

Common factor :

(2x+1)3×4(5x−1)3×5+(5x−1)4×3(2x+1)2×2

Answer 1

\[(2x+1)3×4(5x−1)3×5+(5x−1)4×3(2x+1)2×2\]

Answer 2

Is this what you mean?
\[(2x+1)^3\cdot 4(5x-1)^3 \cdot 5+(5x-1)^4 \cdot 3(2x+1)^2 \cdot 2 \]

Answer 3

ohh yes you're right !
it wouldn't let me paste the equation right

Answer 4

Ok So we have two terms
Do you see what they both have in common?

Answer 5

so what just \[(2x+1) ^3 \times 4 (5x-1)^3 \times 5 \] has in common ?

Answer 6

What does that term you just wrote have in common with that second term ?

Answer 7

\[(5x-1)^3, (2x+1)^2\] are both in common

Answer 8

yes so we can factor that out

Answer 9

For example:
\[a^3 \cdot 4b^3 \cdot 5+b^4\cdot 3 a^2 \cdot 2\]
Both of the terms in this expression have the following factors in common:
\[2,a^2,b^3\]
So we can factor these common factors out but doing so we just divide each term we factored it from by those factors
So like this
\[2a^2b^3( \frac{a^3 \cdot 4 b^3 \cdot 5}{2a^2b^3}+\frac{b^4 \cdot 3a^2 \cdot 2}{2a^2b^3})\]
\[2a^2b^3(a \cdot 2 \cdot 5+b \cdot 3 )\]

Answer 10

And of course you can multiply 2 and 5 to simplify

Answer 11

here's the actual problem with the solution two on page two. http://sh.triton.net/Math/mcv/Derivatives/chain_rule_short_way.pdf

so this would be the chain rule, right ?

Answer 12

the fact that you changed the variables to a and b

Answer 13

I was doing an example

Answer 14

no i know i was just talking about the method

Answer 15

..Do you mean your problem?
That is product + chain rule

Answer 16

okay so for the problem i have so far would this be correct ?
\[a^3 \times 4b^3 + b^4 \times 3a^2 \times 2\]

Answer 17

Assuming you are using a substitution, no
In the first term you are missing a factor 5.
Do you need me to check your derivative too?

Answer 18

oh yeah the five is missing

Answer 19

so would i need to derive this from here on ?

Answer 20

derive?

Answer 21

Do you mean factor?

Answer 22

i'm actually really confused, i dont know what to do from here at all

Answer 23

Do you want to factor?
Well you told me what those two terms had in common which was 2,a^2,b^3
Correct?
Well factor those out like I did above for you

Answer 24

oh alright 1

Answer 25

\[a^2 (a+3) + b^3 (b+ 4 \times 5) \]

Answer 26

is that right ?

Answer 27

No I will draw it.
Give me a moment.

Answer 28

okay

Answer 29

Omg THANK YOU SO MUCH !

Answer 30

i have an exam tomorrow and i was rusty on this topic, i think i understand it now

Answer 31

Keep practicing :)