# Find the Quadratic Constant of Variation 8x^2y-4xy=4xy 8x2y-4xy=4xy
Move all terms containing y to the left side of the equation.
Subtract 4xy from both sides of the equation.
8x2y-4xy-4xy=0
Subtract 4xy from -4xy.
8x2y-8xy=0
8x2y-8xy=0
Factor 8xy out of 8x2y-8xy.
Factor 8xy out of 8x2y.
8xy(x)-8xy=0
Factor 8xy out of -8xy.
8xy(x)+8xy(-1)=0
Factor 8xy out of 8xy(x)+8xy(-1).
8xy(x-1)=0
8xy(x-1)=0
Divide each term by 8x(x-1) and simplify.
Divide each term in 8xy(x-1)=0 by 8x(x-1).
8xy(x-1)8x(x-1)=08x(x-1)
Simplify 8xy(x-1)8x(x-1).
Cancel the common factor of 8.
Cancel the common factor.
8xy(x-1)8x(x-1)=08x(x-1)
Rewrite the expression.
xy(x-1)x(x-1)=08x(x-1)
xy(x-1)x(x-1)=08x(x-1)
Cancel the common factor of x.
Cancel the common factor.
xy(x-1)x(x-1)=08x(x-1)
Rewrite the expression.
y(x-1)x-1=08x(x-1)
y(x-1)x-1=08x(x-1)
Cancel the common factor of x-1.
Cancel the common factor.
y(x-1)x-1=08x(x-1)
Divide y by 1.
y=08x(x-1)
y=08x(x-1)
y=08x(x-1)
Simplify 08x(x-1).
Cancel the common factor of 0 and 8.
Factor 8 out of 0.
y=8(0)8x(x-1)
Cancel the common factors.
Factor 8 out of 8x(x-1).
y=8(0)8(x(x-1))
Cancel the common factor.
y=8⋅08(x(x-1))
Rewrite the expression.
y=0x(x-1)
y=0x(x-1)
y=0x(x-1)
Divide 0 by x(x-1).
y=0
y=0
y=0
The given equation y=0 can not be written as y=kx2, so y doesn’t vary directly with x2.
y doesn’t vary directly with x
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