Question

Factorise ( 2xy-2xz-y+2)

Answer 1

To factor the expression \( 2xy - 2xz - y + 2 \), we can start by grouping the terms.

1. Group the terms:
\[
(2xy - 2xz) + (-y + 2)
\]

2. Factor out common factors in each group:
\[
2x(y - z) - 1(y - 2)
\]

Now we rewrote the second part correctly. This step won't directly help, but let's rewrite it correctly in the following way:

Notice we can write \(2\) as \(2(1)\), so we regroup again:

\[
2xy - 2xz - y + 2 = 2xy - 2xz - (y - 2)
\]

3. However, we should be straightforward about combining the factors carefully. Let’s rewrite the combined terms:

Reorganizing directly gives us:
\[
2x(y-z) - 1(y-2)
\]
4. Collect \(y - z\) and \(y - 2\):
\[
= (2x - 1)(y - 2) + 2(z)
\]

Now we see the direct rewrite but trying another step:

Combine factored form:
\[
= (2x - 1)(y - 2)
\]

This reflects a full combination:
\[
= (2x - 1)(y - 2)
\]

So, putting it all together, and clarifying, we can now say we can achieve:
\[
2xy - 2xz - y + 2 = (2x - 1)(y - 2)
\]

Therefore, the final factorized form of \(2xy - 2xz - y + 2\) is:
\[
(2x - 1)(y - 2)
\]