SOLUTION: 1. If the area of a square garden is (x 2 + 8x + 16) sq units, is it possible to find the measure of its side? Why? Or why not? How? 2. If the area of a garden is (3x 2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1. If the area of a square garden is (x 2 + 8x + 16) sq units, is it possible to find the measure of its side? Why? Or why not? How? 2. If the area of a garden is (3x 2       Log On


   

Question 622680: 1. If the area of a square garden is (x
2
+ 8x + 16) sq units, is it possible to find the measure of its side? Why? Or why
not? How? 2. If the area of a garden is (3x
2
+ 8x + 4) sq units, is it possible to find the measure of the side? Is the garden a
square? Why? Or why not?
3. Is x
2
– y
2
= (x – y)
2
? Explain why or why not. If you do not understand the rules on factoring , what
do you think will happen?
4. What is the difference of the squares of 105 and 5 ? What is the square of their difference?
5. Explain or illustrate how you can find the difference of the squares of two terms using 105 and 5.


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1. x%5E2%2B8x%2B16 Factor:
%28x%2B4%29%28x%2B4%29
Yes because the given quadratic expression is a perfect square which can be shown by factoring.
2. 3x%5E2%2B8x%2B4 Factor:
%283x%2B2%29%28x%2B2%29 Yes! The sides are %283x%2B2%29 and %28x%2B2%29 and the garden is not a square because the sides are not equal.
3. Is x%5E2-y%5E2+=+%28x-y%29%5E2?
To find out, expand the right side:
%28x-y%29%5E2+=+%28x-y%29%28x-y%29=x%5E2-2xy%2By%5E2
x%5E2-y%5E2+=+%28x%2By%29%28x-y%29
So %28x-y%29%5E2+%3C%3E+x%5E2-y%5E2
4.
a) 105%5E2-5%5E2+=+11025-25=11000
b) %28105-5%29%5E2+=+%28100%29%5E2=10000
5. Use the identity:
%28a%5E2-b%5E2%29+=+%28a-b%29%28a%2Bb%29 and if a = 105 and b = 5, then...
105%5E2-5%5E2+=+%28105-5%29%28105%2B5%29=%28100%29%28110%29=11000