I don't know whether it's y^2-3y+2+3y-4y-5 or 2y-3y+2+3y-4y-5, so I'll do both.
y^2-3y+2+3y-4y-5
y^2+(-3y+3y-4y)+(2-5); group them together
y^2+(-4y)+(-3)
y2-4y-3
OR
2y-3y+2+3y-4y-5
(2y-3y+3y-4y)+(2-5); group them together
(-2y)+(-3)
-2y-3
88 + 5y - y2 66 - 3y + y2 Subtract: 22 + 8y -2y2
5
y2 + 8y + 16 = y2 + 4y + 4y + 16 = y(y + 4) + 4(y + 4) = (y + 4)(y + 4) or (y + 4)2
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.
3x2+6xy+3y2= 3(x2+2xy+y2)= 3(x+y)2
88 + 5y - y2 66 - 3y + y2 Subtract: 22 + 8y -2y2
x2 -y2 +4y-4=(x+y)(x-y)+4y-4
(2-r)e-rr
x2 + 3y = 7 3x + y2 = 3 3y = x2 + 7 y2 = -3x + 3 y = x2/3 + 7/3 y = ± √(-3x + 3) If you draw the graphs of y = x2/3 + 7/3 and y = ± √(-3x + 3) in a graphing calculator, you will see that they don't intersect, so that the system of the given equations has not a solution.
3y4 + 3y2 = 3y2(y2 + 1)
5
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
y2 + 8y + 16 = y2 + 4y + 4y + 16 = y(y + 4) + 4(y + 4) = (y + 4)(y + 4) or (y + 4)2
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.
All you can do to factor that expression is to divide both terms by y: y2 + 4y = y(y + 4)
There are an infinite number of them. Here are a few: y = 4 y = 2 + 2 3y = 12 4y + 7 = 5y + 3 y2 - 9y + 20 = 0 y3 + 2y2 -3y + 13 = 5y2 + 3y + 5
factor 4y - 32