iwillrektyou
  • iwillrektyou
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.
Mathematics
chestercat
  • chestercat
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TheSmartOne
  • TheSmartOne
For #1, use the formula: \(\sf a^2-b^2 = (a-b)(a+b)\)
iwillrektyou
  • iwillrektyou
I did number 1, but I am highly doubtful of my answer. Number 2 is confusing me a little.
TheSmartOne
  • TheSmartOne
What answer did you get?

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iwillrektyou
  • iwillrektyou
I factored out the GCF and couldn't factor it out further, so I got: 9[9x^2 - 4y^2]
TheSmartOne
  • TheSmartOne
How did you even get 9?? Use the formula I gave you (:
iwillrektyou
  • 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. :)
TheSmartOne
  • TheSmartOne
49 is a perfect square. Its only factors are: 1, 7, 49
iwillrektyou
  • iwillrektyou
Oh shoot careless mistake.
iwillrektyou
  • iwillrektyou
Thanks for pointing it out.
TheSmartOne
  • 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 :)
iwillrektyou
  • iwillrektyou
I think I understand the next problem now, I just factor it out (hopefully no careless mistakes this time!)
TheSmartOne
  • TheSmartOne
we're not done with #1 yet :p
iwillrektyou
  • iwillrektyou
QQ Okay.
iwillrektyou
  • iwillrektyou
(7x - 6y) (7x + 6y)?
TheSmartOne
  • TheSmartOne
correct :)
iwillrektyou
  • iwillrektyou
Thanks for the help! This is the answer for #1?
TheSmartOne
  • TheSmartOne
For your second question, do you know how to group factor?
iwillrektyou
  • iwillrektyou
Yes, I think so.
TheSmartOne
  • TheSmartOne
and it is :)
TheSmartOne
  • TheSmartOne
Let me show you an example of group factoring \(\sf ax + bx + ay + by = x(a+b) + y(a+b) = (x+y)(a+b)\)
iwillrektyou
  • iwillrektyou
Oh yes, I do know how. Can you check my work/answers after I'm done?
TheSmartOne
  • TheSmartOne
sure :) I'd love to (:
iwillrektyou
  • 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)
TheSmartOne
  • TheSmartOne
correct :)
iwillrektyou
  • iwillrektyou
Thank you so much for helping me and spending time to read this!!:D
TheSmartOne
  • TheSmartOne
anytime :)

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