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.
(y-6)(y-4) y x y = y2 y x -4 = -4y y x -6 = -6y -4 x -6 = 24 y2 - 4y - 6y + 24 y2 - 10y + 24
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-5y^2+(-3y+3y-4y)+(2-5); group them togethery^2+(-4y)+(-3)y2-4y-3OR2y-3y+2+3y-4y-5(2y-3y+3y-4y)+(2-5); group them together(-2y)+(-3)-2y-3
I would clean that up a little bit to make it look like, y^2+4y-4. which will factor out into, (y+2)*(y-2) So the two possible answers is -2 and 2
factor 4y - 32
x2 -y2 +4y-4=(x+y)(x-y)+4y-4
All you can do to factor that expression is to divide both terms by y: y2 + 4y = y(y + 4)
y2 + 8y + 16 = y2 + 4y + 4y + 16 = y(y + 4) + 4(y + 4) = (y + 4)(y + 4) or (y + 4)2
9y-81=9*(y-9)
4y2 + 16y + 16 = 4(y2 + 4y + 4) = 4(y2 + 2y + 2y + 2) = 4[y(y + 2) + 2(y + 2)] = 4(y + 2)2
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
The difference of cubes has a formula. (4x - y)(16x2 + 4xy + y2)
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.
It is: y2
y2 + 4y -12 = 0 y2 + 6y - 2y -12 = 0 y(y + 6) -2(y +6) = 0 (y -2) x (y + 6) = 0 Hence (y-2) is zero which gives y = 2 or (y + 6) is zero which gives y = -6 The roots or solutions to the equation y2 + 4y -12 = 0 are y = 2 and y = -6
(y-6)(y-4) y x y = y2 y x -4 = -4y y x -6 = -6y -4 x -6 = 24 y2 - 4y - 6y + 24 y2 - 10y + 24