Question

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.

Answer 1

For #1, use the formula:

\(\sf a^2-b^2 = (a-b)(a+b)\)

Answer 2

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

Answer 3

What answer did you get?

Answer 4

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

Answer 5

How did you even get 9??

Use the formula I gave you (:

Answer 6

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. :)

Answer 7

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

Answer 8

Oh shoot careless mistake.

Answer 9

Thanks for pointing it out.

Answer 10

\(\sf a^2-b^2 = (a-b)(a+b)\)

\(\sf 49x^2 - 36y^2 = (7x)^2 - (6y)^2\)

Thus, implying that:
\(\sf a \to 7x\)
\(\sf b \to 6y\)

Plug it into the formula :)

Answer 11

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

Answer 12

we're not done with #1 yet :p

Answer 13

QQ Okay.

Answer 14

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

Answer 15

correct :)

Answer 16

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

Answer 17

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

Answer 18

Yes, I think so.

Answer 19

and it is :)

Answer 20

Let me show you an example of group factoring

\(\sf ax + bx + ay + by = x(a+b) + y(a+b) = (x+y)(a+b)\)

Answer 21

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

Answer 22

sure :)

I'd love to (:

Answer 23

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

Answer 24

correct :)

Answer 25

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

Answer 26

anytime :)