Factor y2 + 10z - 10y - yz.
re-write as y^2-10y-yz+10z and factor 2 and 2
y(y-10)-z(y-10)
(y-z)(y-10)
To factor the expression y^2 + 10z - 10y - yz, we can use the technique known as "grouping."
Step 1: Group the terms
Group the terms with common factors. In this case, we can group the terms as follows:
(y^2 - 10y) + (10z - yz)
Step 2: Factor out the common factors from each group
From the first group, we can factor out y:
y(y - 10)
From the second group, we can factor out z:
z(10 - y)
Step 3: Rearrange the terms to get the final factorization
Rearranging the terms, we have:
y(y - 10) + z(10 - y)
Step 4: Simplify
To simplify further, we can distribute the negative sign in the second term:
y(y - 10) - z(y - 10)
Now, notice that we have a common factor of (y - 10) in both terms. We can factor that out:
(y - 10)(y - z)
Therefore, the fully factored form of the expression y^2 + 10z - 10y - yz is (y - 10)(y - z).