Cristian M. answered • 08/08/20
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Just a notation observation: I don't know why the problem talks about side lengths of ax + b since no x's are used in the expression for area, so there should be no "x" in the final answer; it will not be 13xy + 10. I think that the original problem should have said "ay + b."
Otherwise, I hope this explanation helps! Please let me know if I can clarify anything presented here.
Cristian M.
I do not know what happened during the processing and upload of this video, but it lost my camera and microphone inputs. I'll explain the work here: Since a square's area is found by multiplying the side length by itself, we can go backwards and say that the side length of a square, given area, is found by taking the square root of the area. Isn't it great how a square has the same side length all four sides?? So, for a polynomial to have a "perfect square root" much like how 16 has a perfect square root of 4, we have to ensure that it can be "square-rooted" cleanly. That's where this formula comes in: (a+b)^2 = a^2 + 2ab + b^2. Here, the area is 169y^2 + 280y + 100 square centimeters. What is a? Look at how 169y^2 breaks up into (13)(13)(y)(y), which can be re-arranged as (13y)(13y). So 13y multiplied by itself is 169y^2. Great! So 13y is our a. Look at 100. What is its square root? 10. Since 10*10 = 100, we can say that 10 is our b. Now, to check if we have a true perfect square trinomial on our hands, we need to try 2ab. What is (2)(13y)(10) ? It is 260y, which is the middle term of the area expression. Everything checks out! So a = 13y, and b= 10. The side length of the square is (13y + 10) cm. I hope this helps.08/08/20