Sure, let's factor the expression [tex]\( xy - 10y - 4x + 40 \)[/tex] by grouping.
1. First, we will look at the given expression: [tex]\( xy - 10y - 4x + 40 \)[/tex].
2. Next, we group the terms to make factoring easier:
[tex]\[
(xy - 10y) + (-4x + 40)
\][/tex]
3. Factor out the common factors from each group:
[tex]\[
y(x - 10) - 4(x - 10)
\][/tex]
4. Notice that each group contains a common binomial factor [tex]\((x - 10)\)[/tex]:
[tex]\[
y(x - 10) - 4(x - 10) = (x - 10)(y - 4)
\][/tex]
Thus, the factored form of the expression [tex]\( xy - 10y - 4x + 40 \)[/tex] is:
[tex]\[
(x - 10)(y - 4)
\][/tex]
