## unimatix one year ago Simplify Algebra (in comments)

1. unimatix

$4(-8)(2-8x)^3(x^2-9)^3+3(2x)(2-8x)^4(x^2-9)^2$

2. unimatix

The next step shown looks like $4(2-8x)^3(x^2-9)^2(20x^2-3x-72)$

3. unimatix

I'm having trouble understand how that was arrived at.

4. anonymous

hold on solving them

5. unimatix

Okay, thanks!

6. anonymous

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7. anonymous

(www.Mathway.com)

8. unimatix

wut?

9. Nnesha

:=)

10. Nnesha

heya

11. Nnesha

take out the common factor

12. unimatix

I just need it simplified to the second step.

13. unimatix

because then I am solving equal to 0.

14. unimatix

that's where my confusion is

15. Nnesha

$4(-8)\color{Red}{(2-8x)^3}\color{blue}{(x^2-9)^3}+3(2x)\color{Red}{(2-8x)^4}\color{blue}{(x^2-9)^2}$ see there is GCF (greatest common factor

16. Nnesha

|dw:1443912816495:dw| now what is common in both terms sorry about the writing ....:/\:

17. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @unimatix The next step shown looks like $4(2-8x)^3(x^2-9)^2(20x^2-3x-72)$ $$\color{blue}{\text{End of Quote}}$$ i think you forgot the negative sign it's -4

18. Nnesha

$4(-8)\color{Red}{(2-8x)^3}\color{blue}{(x^2-9)^3}+3(2x)\color{Red}{(2-8x)^4}\color{blue}{(x^2-9)^2}$ (x^2-9)^3 can be wriitten as (x^2-9)^2(x^2-9) $4(-8)\color{Red}{(2-8x)^3}\color{blue}{(x^2-9)^2(x^2-9)}+3(2x)\color{Red}{(2-8x)^4}\color{blue}{(x^2-9)^2}$ so as you can (x^2-9)^2 is common

19. Nnesha

ohhh well you're not online can't work without u

20. mathstudent55

$$4(-8)(2-8x)^3(x^2-9)^3+3(2x)(2-8x)^4(x^2-9)^2$$ $$=-32(2-8x)^3(x^2-9)^3+3(2x)(2-8x)^4(x^2-9)^2$$ $$=(2 - 8x)^3(x^2 - 9)^2[-32(x^2-9)+3(2x)(2-8x)]$$ $$=(2 - 8x)^3(x^2 - 9)^2[-32x^2+288+12x - 48x^2]$$ $$=(2 - 8x)^3(x^2 - 9)^2(-80x^2+12x + 288)$$

21. unimatix

3rd line down I'm confused

22. unimatix

How are you moving the -32?

23. mathstudent55

$$=(2 - 8x)^3(x^2 - 9)^2(-80x^2+12x + 288)$$ $$= -4 (2 - 8x)^3(x^2 - 9)^2(20x^2 -3 x - 72)$$

24. mathstudent55

Here is the second line. You're ok with it? $$=-32(2-8x)^3(x^2-9)^3+3(2x)(2-8x)^4(x^2-9)^2$$

25. unimatix

Yeah!

26. mathstudent55

From the 2nd line to the third line, we factor out two factors: $$=-32\color{red}{(2-8x)^3}\color{purple}{(x^2-9)^3}+3(2x)\color{red}{(2-8x)^4}\color{purple}{(x^2-9)^2}$$

27. mathstudent55

We have (in red) the factor 2 - 8x. It is to the 3 power in the first part, and to the 4th power in the second part. We can factor out (8 - 2x)^3. Then (in purple) we have the factor x^2 - 9 to the 3rd power and to the 2th power. We can factor out (x^2 - 9)^2. Ok so far?

28. unimatix

OKay I understand that step

29. unimatix

good on the 4th line too

30. unimatix

Okay I got it.

31. mathstudent55

Here is the 3rd line after factoring out those two factors: $$=\color{red}{(2 - 8x)^3}\color{purple}{(x^2 - 9)^2}[-32\color{purple}{(x^2-9)}+3(2x)\color{red}{(2-8x)}]$$

32. mathstudent55

Ok.

33. unimatix

I'm not really used to factoring out those factors I guess.

34. mathstudent55

Then the 5th line is just simplification inside the square brackets.

35. unimatix

That all makes sense. It's pretty straightforward. Thank you!

36. mathstudent55

Finally the last line which is on the next response above, is simply taking out a factor of -4 from inside the parentheses and bringing it out.

37. mathstudent55

You're welcome.