Use the difference of squares factorization - that for any numbers a and b, (a-b)(a+b)=a^2-b^2.
We have:
(x^2+1)(x^2-1)=x^4-1
In addition:
(x-1)(x+1)=x^2-1, so we have:
(x^2+1)(x+1)(x-1)
As our complete factorization.
The general equation of a circle is

where a and b are the x and y components of the center respectively.
In order to get into this format, we have to use a method that I'm drawing a blank on the same, my apologies about that.
Anyway, what you want is to first isolate the variable on side so now you have:

(you'll see why I rearranged this soon)
Now you have to make it into an equation that can be simplified into the format stated earlier.
So, You have to take the x & y terms (-4x & -8y in this case) divide them each by two, and then square them.
The result of this step is the equation:
Notice the new components that have been added (4 & 16) and how the have been
added to both sides. That is an important step.
Now we simplify and get:

So the coordinate of the center is: (2,4) and the radius is 5
Answer:
3 pieces
Step-by-step explanation:
Given: Figure
To find: Number of 8.5 in. × 11 in. pieces used to cover the floors of a room and a hallway in her dollhouse
Solution:
In the given figure, AC = 22 in.
AB + BC = 22 in.
AB + EF = 22 (As BC = EF being opposite sides of rectangle)
AB + 10 = 22
AB = 22 - 10 = 12 in.
Area of rectangle ABGH = AB × AH = 12 × 5 = 60 square inches
(area of rectangle = length × breadth )
CE = CD + DE = AH + GF (As CD = AH and DE = GF)
CE = 5 + 15 = 20 inches
Area of rectangle BCEF = BC × CE = 10 × 20 = 200 square inches
(BC = EF = 10 in.)
Total area of the figure = Area of rectangle ABGH + Area of rectangle BCEF = 60 + 200 = 260 square inches
Area of pieces of felt = 8.5 × 11
So,
Number of pieces required = Total area of the figure / Area of pieces of felt =
3 pieces
Answer:
This is impossible.
Step-by-step explanation:
The interior angle of a regular polygon is equal to

where n is the number of sides.
Setting this equal to 180°,

which is false.