7zyz2-y2+3z-yz+y

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=z and b=y.

7zy(z+y)(z-y)+3z-yz+y

To write 3z-yz+y as a fraction with a common denominator, multiply by z-yz-y.

7zy(z+y)(z-y)+3z-yz+y⋅z-yz-y

Multiply 3z-yz+y and z-yz-y.

7zy(z+y)(z-y)+(3z-y)(z-y)(z+y)(z-y)

Combine the numerators over the common denominator.

7zy+(3z-y)(z-y)(z+y)(z-y)

7zy+(3z-y)(z-y)(z+y)(z-y)

Expand (3z-y)(z-y) using the FOIL Method.

Apply the distributive property.

7zy+3z(z-y)-y(z-y)(z+y)(z-y)

Apply the distributive property.

7zy+3z⋅z+3z(-y)-y(z-y)(z+y)(z-y)

Apply the distributive property.

7zy+3z⋅z+3z(-y)-yz-y(-y)(z+y)(z-y)

7zy+3z⋅z+3z(-y)-yz-y(-y)(z+y)(z-y)

Simplify and combine like terms.

Simplify each term.

Multiply z by z by adding the exponents.

Move z.

7zy+3(z⋅z)+3z(-y)-yz-y(-y)(z+y)(z-y)

Multiply z by z.

7zy+3z2+3z(-y)-yz-y(-y)(z+y)(z-y)

7zy+3z2+3z(-y)-yz-y(-y)(z+y)(z-y)

Rewrite using the commutative property of multiplication.

7zy+3z2+3⋅-1(zy)-yz-y(-y)(z+y)(z-y)

Multiply 3 by -1.

7zy+3z2-3(zy)-yz-y(-y)(z+y)(z-y)

Multiply y by y.

7zy+3z2-3zy-yz-1⋅-1y2(z+y)(z-y)

Multiply -1 by -1.

7zy+3z2-3zy-yz+1y2(z+y)(z-y)

Multiply y2 by 1.

7zy+3z2-3zy-yz+y2(z+y)(z-y)

7zy+3z2-3zy-yz+y2(z+y)(z-y)

Subtract yz from -3zy.

Move z.

7zy+3z2-3yz-yz+y2(z+y)(z-y)

Subtract yz from -3yz.

7zy+3z2-4yz+y2(z+y)(z-y)

7zy+3z2-4yz+y2(z+y)(z-y)

7zy+3z2-4yz+y2(z+y)(z-y)

Subtract 4yz from 7zy.

Move z.

3z2+7yz-4yz+y2(z+y)(z-y)

Subtract 4yz from 7yz.

3z2+3yz+y2(z+y)(z-y)

3z2+3yz+y2(z+y)(z-y)

3z2+3yz+y2(z+y)(z-y)

Combine (7zy)/(z^2-y^2)+(3z-y)/(z+y)