Question

Part A: The area of a square is (25x2 - 20x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.

Part B: 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.

Part C: 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

@Gebooors

Answer 2

Try (5x-2)^2

Answer 3

what part is that for? try that for what? why ?

Answer 4

That is for A

Answer 5

can you elaborate

Answer 6

Side of square is 5x -2, sides are equal.
Try to calculate (5x -2)^2
You can use binomical expansion

Answer 7

i really dont and cannot

Answer 8

understand at least

Answer 9

Are you familiar with (a+b)^2 = a^2 + 2ab + b^2

Answer 10

Then (a -b) ^2 = a^2 -2ab + b^2

Answer 11

no /:

Answer 12

And third one (a +b) (a - b)= a^2 -b^2

Answer 13

I'll show you:

Answer 14

(5x -2)^2 =(5x -2)(5x -2) =
5x * 5x + 5x *(-2) + (-2) * 5x+ (-2)(-2)
Can you continue from here?

Answer 15

not really

Answer 16

You start to Multiply: 5x * 5x = 25*x^2

Answer 17

25x=25x2

Answer 18

@tkhunny

Answer 19

Are you going to work on it, this time?

Answer 20

(25x2 - 20x + 4) This should be recognized as a perfect square trinomial. As a perfect square, the pieces had better be the square roots of the terms we already have.

25x^2 ==> 5x
4 ==> 2

Thus (5x + 2)^2 and 5x+2 is the length of the side of the square.

Answer 21

thats it for part a ? @tkhunny

Answer 22

and what about part b

Answer 23

For part B, you must recognize the Difference of Squares and factor it as such. It wirks like this.

\((a^{2} - b^{2}) = (a+b)(a-b)\)

Go!

Answer 24

lol good one

Answer 25

You may wish to consider factoring by grouping.

x3 + 2x2 - 9x - 18

x^2(x+2) - 9(x+2) = (x^2 - 9)(x+2)

Finally, your task is to recognize the difference of squares and continue with the factoring - just like the last problem.

Answer 26

(7x-6y)(7x+6y) -- That is correct.

Answer 27

I regret that I get only one Medal per thread. EXCELLENT work.

Learn a little more mathematics and you will be able to tell when your accountant and money manager are trying to rip you off and blow all your hard-earned millions.

Answer 28

i only know the answers cuz i got them from someone else lol however i know absolutely nothing about this very fun very useful math

Answer 29

...and I thought we were getting along a little better, this time. {wry smile}{tiny chuckle}

Answer 30

oh no, never with math in the way

Answer 31

Tk, notice how 25x^2 - 20x + 4 has a minus sign,

√25x^2 = 5x

√4 = 2

(5x - 2)^2 = (5x)^2 -2(5x)(2) - (2)^2
= 25x^2 -20x + 4 \(\ \color{green}\checkmark\)

Answer 32

Whoops! So it does. Good call.