# Simplify square root of (z^2-2zy+y^2)(z+y)^2 (z2-2zy+y2)(z+y)2
Factor using the perfect square rule.
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅z⋅(-y)
Simplify.
2ab=-2zy
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=z and b=-y.
(z-y)2(z+y)2
(z-y)2(z+y)2
Rewrite (z-y)2(z+y)2 as ((z-y)(z+y))2.
((z-y)(z+y))2
Pull terms out from under the radical, assuming positive real numbers.
(z-y)(z+y)
Expand (z-y)(z+y) using the FOIL Method.
Apply the distributive property.
z(z+y)-y(z+y)
Apply the distributive property.
z⋅z+zy-y(z+y)
Apply the distributive property.
z⋅z+zy-yz-y⋅y
z⋅z+zy-yz-y⋅y
Simplify terms.
Combine the opposite terms in z⋅z+zy-yz-y⋅y.
Reorder the factors in the terms zy and -yz.
z⋅z+yz-yz-y⋅y
Subtract yz from yz.
z⋅z+0-y⋅y
Add z⋅z and 0.
z⋅z-y⋅y
z⋅z-y⋅y
Simplify each term.
Multiply z by z.
z2-y⋅y
Multiply y by y by adding the exponents.
Move y.
z2-(y⋅y)
Multiply y by y.
z2-y2
z2-y2
z2-y2
z2-y2
Simplify square root of (z^2-2zy+y^2)(z+y)^2

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