Question

2y² + az - 2z+ ay²

How do I factor this equation?

Answer 1

`y^2(2 + a) + z(a-2)`

Explanation:

To factor the equation...

`2y^2 + az - 2z+ ay^2`

First, we can group like terms:

`(2y^2 + ay^2) + (az - 2z)`

Notice how the terms in the left expression in parentheses both share a
`y^2`, and the terms in the right expression in parentheses both share a
`z`.

So next, we can factor out (undistribute) those shared factors:

`\boxed{y^2(2 + a) + z(a-2)}`

Further Note

There is no way to further factor this equation. However, if the expression in parentheses on the right had been the same as the expression in parentheses on the left, we could have combined them using the distributive property:

`y^2(2 + a) + z(2 + a)`

`= (2 + a)(y^2 + z)`

because
`a(b + c) \Leftrightarrow ab + ac`.