x2 -y2 +4y-4=(x+y)(x-y)+4y-4
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factor 4y - 32
All you can do to factor that expression is to divide both terms by y: y2 + 4y = y(y + 4)
(x - y)(x + y)(x2 - xy + y2)(x2 + xy + y2)
y2=-x2-8x+6
x2 - y2 + 9x - 9y =(x2 + 9x) - (y2 + 9y) =x(x + 9) - y(y + 9)================================Another way to go after it:x2 - y2 + 9x - 9y =(x2 - y2) + 9x - 9y =(x + y) (x - y) + 9 (x - y) =(x + y + 9) (x - y)
Complete the squares: x2 - 10x + 25 + y2 + 4y + 4 - 52 = 25 + 4 = 29 x2 - 10x + 25 + y2 + 4y + 4 = 52 + 29 = 81 So the radius is sqrt(81) = 9
Given: x2 + y2 - 10x + 4y + 4 = 0 First, we'll move our constants to the right: x2 + y2 - 10x + 4y = -4 Then group terms with the same variables together: x2 - 10x + y2 + 4y = -4 Then complete the squares: x2 - 10x + 25 + y2 + 4y + 4 = -4 + 25 + 4 (x - 5)2 + (y + 2)2 = 25 And there we have it. This is an equation for a circle whose center point is at (5, -2), with a radius of √25, which equals 5.
(2-r)e-rr
factor 4y - 32
x2 + y2 - 10x + 4y - 52 = 0 x2 - 10x + y2 + 4y = 52 Complete the square (x2 - 10x + 25) + (y2 + 4y + 4) = 52 + 25 + 4 (x - 5)2 + (y + 2)2 = 81 (x - 5)2 + (y - -2)2 = 92 This is the equation of a circle with center (5, -2), and radius 9.
All you can do to factor that expression is to divide both terms by y: y2 + 4y = y(y + 4)
(x2 - xy + y2)(x + y)
y2 + 8y + 16 = y2 + 4y + 4y + 16 = y(y + 4) + 4(y + 4) = (y + 4)(y + 4) or (y + 4)2
(x - y + 7)(x + y)
x2 + 2y - 6x + 8y - 1 = x2 - y2 + 4x + 6y - 1 y2 - 10x + 4y = 0 y(y+4) = 10x It cannot be solved completely because with two variables (x and y) you need two independent equations for a full solution.
X2+y2=25 (x-8)2+y2 =41
Given: x2 + y2 - 6x + 4y = -4 We'll start by rearranging for clarity: x2 - 6x + y2 + 4y + 4= 0 We can already get a perfect square with our y-value, so let's do that x2 - 6x + (y + 2)2 = 0 Now to get x down to one term, you need to complete the square: x2 - 6x + 9 + (y + 2)2 = 9 (x - 3)2 + (y + 2)2 = 32 And that gives you the answer. The circle has a center point of (3, -2), and a radius of 3.