Question

Find the simplest factored form of 30x^2(2x+1)^2-10x(2x+1)^3

Answer 1

Substitute let u =2x+1 and rewrite

Answer 2

I can't do it like that I have to factor out the LCD

Answer 3

yes you can
\[30x^2u^2-10xu^3\]

Answer 4

That's easier to see yes? just remember you have to back subsitute

Answer 5

lcd is
\[10xu^ 2 or 10x(2x+1)^2\]

Answer 6

\[30x^2u^2-10xu^3=10xu^2(3x-u)\] yes?

Answer 7

then plug 2x+1 back in for u and simplify

Answer 8

I wish I could do u -sub but it's mandatory that we factor the LCD

Answer 9

This is what I got

Answer 10

you are factoring the lcd, youre just calling it U instead of 2x+1

Answer 11

U is not in the final answer, you have to go back and put in 2x+1 where all the u's are

Answer 12

10x[3x(2x+1)^2-1(2x+1)^3]
=10x(2x+1)^2(3x-1)

Answer 13

i almost got the same thing i got (x-1) in the final term

Answer 14

Yeah that's my mistake,

Answer 15

I don't know what I did wrong?

Answer 16

let me show you how i did it. watch with U substitution (trust me its easier and its ok to do)

Answer 17

Okay

Answer 18

wait I'll try to do it without U substituion but its harder and more typing.

Answer 19

\[30x^2(2x+1)^2-10x(2x+1)^3=10x(2x+1)^2(3x-2x+1)\]

Answer 20

oops the last 2x+1 should be in parenthesis, hence -1 instead of +1 in the last term

Answer 21

Same way but let U = 2x+1
\[30x^2u^2-10xu^3=10xu^2(3x-u)\]

back substitute u = 2x+1

\[10x(2x+1)^2(3x-2x-1)=10x(2x+1)^2(x-1)\]

Answer 22

make sense?

Answer 23

Yes, thanks

Answer 24

yw

Answer 25

i might have another problem like that if you want to try one on your own

Answer 26

Sure

Answer 27

A LOT of problems like this are factored in calculus derivatives, so its good to know how to factor these types of problems. Lets see:

ok this one is a bit harder but I think you can do it. Factor

\[(x-y)^4-4(x-y)^2\]