# Divide (12x^2y^2+8xy^2-8y^2)/(2x^2y)

12x2y2+8xy2-8y22x2y
Factor 4y2 out of 12x2y2+8xy2-8y2.
Factor 4y2 out of 12x2y2.
4y2(3×2)+8xy2-8y22x2y
Factor 4y2 out of 8xy2.
4y2(3×2)+4y2(2x)-8y22x2y
Factor 4y2 out of -8y2.
4y2(3×2)+4y2(2x)+4y2(-2)2x2y
Factor 4y2 out of 4y2(3×2)+4y2(2x).
4y2(3×2+2x)+4y2(-2)2x2y
Factor 4y2 out of 4y2(3×2+2x)+4y2(-2).
4y2(3×2+2x-2)2x2y
4y2(3×2+2x-2)2x2y
Cancel the common factor of 4 and 2.
Factor 2 out of 4y2(3×2+2x-2).
2(2y2(3×2+2x-2))2x2y
Cancel the common factors.
Factor 2 out of 2x2y.
2(2y2(3×2+2x-2))2(x2y)
Cancel the common factor.
2(2y2(3×2+2x-2))2(x2y)
Rewrite the expression.
2y2(3×2+2x-2)x2y
2y2(3×2+2x-2)x2y
2y2(3×2+2x-2)x2y
Cancel the common factor of y2 and y.
Factor y out of 2y2(3×2+2x-2).
y(2y(3×2+2x-2))x2y
Cancel the common factors.
Factor y out of x2y.
y(2y(3×2+2x-2))yx2
Cancel the common factor.
y(2y(3×2+2x-2))yx2
Rewrite the expression.
2y(3×2+2x-2)x2
2y(3×2+2x-2)x2
2y(3×2+2x-2)x2
Apply the distributive property.
2y(3×2)+2y(2x)+2y⋅-2×2
Simplify.
Rewrite using the commutative property of multiplication.
2⋅3(yx2)+2y(2x)+2y⋅-2×2
Rewrite using the commutative property of multiplication.
2⋅3(yx2)+2⋅2(yx)+2y⋅-2×2
Multiply -2 by 2.
2⋅3(yx2)+2⋅2(yx)-4yx2
2⋅3(yx2)+2⋅2(yx)-4yx2
Simplify each term.
Multiply 2 by 3.
6(yx2)+2⋅2(yx)-4yx2
Multiply 2 by 2.
6yx2+4yx-4yx2
6yx2+4yx-4yx2
Split the fraction 6yx2+4yx-4yx2 into two fractions.
6yx2+4yxx2+-4yx2
Split the fraction 6yx2+4yxx2 into two fractions.
6yx2x2+4yxx2+-4yx2
Cancel the common factor of x2.
Cancel the common factor.
6yx2x2+4yxx2+-4yx2
Divide 6y by 1.
6y+4yxx2+-4yx2
6y+4yxx2+-4yx2
Cancel the common factor of x and x2.
Factor x out of 4yx.
6y+x(4y)x2+-4yx2
Cancel the common factors.
Factor x out of x2.
6y+x(4y)x⋅x+-4yx2
Cancel the common factor.
6y+x(4y)x⋅x+-4yx2
Rewrite the expression.
6y+4yx+-4yx2
6y+4yx+-4yx2
6y+4yx+-4yx2
Move the negative in front of the fraction.
6y+4yx-4yx2
Divide (12x^2y^2+8xy^2-8y^2)/(2x^2y)