## iwillrektyou one year ago 1. The area of a rectangle is (49x2 - 36y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (2 points) 2. The volume of a rectangular box is (x3 + 2x2 - 9x - 18) cubic units. Determine the dimensions of the rectangular box by factoring the volume expression completely. Show your work.

1. TheSmartOne

For #1, use the formula: $$\sf a^2-b^2 = (a-b)(a+b)$$

2. iwillrektyou

I did number 1, but I am highly doubtful of my answer. Number 2 is confusing me a little.

3. TheSmartOne

What answer did you get?

4. iwillrektyou

I factored out the GCF and couldn't factor it out further, so I got: 9[9x^2 - 4y^2]

5. TheSmartOne

How did you even get 9?? Use the formula I gave you (:

6. iwillrektyou

I have no idea. I just used 9 because it was a common factor between 49 and 36. I will use your formula, thank you. :)

7. TheSmartOne

49 is a perfect square. Its only factors are: 1, 7, 49

8. iwillrektyou

Oh shoot careless mistake.

9. iwillrektyou

Thanks for pointing it out.

10. TheSmartOne

$$\sf a^2-b^2 = (a-b)(a+b)$$ $$\sf 49x^2 - 36y^2 = (7x)^2 - (6y)^2$$ Thus, implying that: $$\sf a \to 7x$$ $$\sf b \to 6y$$ Plug it into the formula :)

11. iwillrektyou

I think I understand the next problem now, I just factor it out (hopefully no careless mistakes this time!)

12. TheSmartOne

we're not done with #1 yet :p

13. iwillrektyou

QQ Okay.

14. iwillrektyou

(7x - 6y) (7x + 6y)?

15. TheSmartOne

correct :)

16. iwillrektyou

Thanks for the help! This is the answer for #1?

17. TheSmartOne

For your second question, do you know how to group factor?

18. iwillrektyou

Yes, I think so.

19. TheSmartOne

and it is :)

20. TheSmartOne

Let me show you an example of group factoring $$\sf ax + bx + ay + by = x(a+b) + y(a+b) = (x+y)(a+b)$$

21. iwillrektyou

Oh yes, I do know how. Can you check my work/answers after I'm done?

22. TheSmartOne

sure :) I'd love to (:

23. iwillrektyou

x^3 + 2x^2 - 9x - 18 x^2(x + 2) -9(x + 2) (x + 2) (x^2 - 9) (x + 2) (x - 3) (x + 3)

24. TheSmartOne

correct :)

25. iwillrektyou

Thank you so much for helping me and spending time to read this!!:D

26. TheSmartOne

anytime :)