Sure, let's simplify the expression [tex]\( a x - 2 b x + 2 a y + 4 b y \)[/tex] step-by-step.
1. Group the terms involving common factors:
[tex]\[
a x - 2 b x + 2 a y + 4 b y
\][/tex]
We can see that there are two terms involving [tex]\( x \)[/tex] and two terms involving [tex]\( y \)[/tex].
2. Factor out the common terms:
[tex]\[
(a x - 2 b x) + (2 a y + 4 b y)
\][/tex]
3. Factor [tex]\( x \)[/tex] from the first grouping and [tex]\( y \)[/tex] from the second grouping:
[tex]\[
x (a - 2 b) + y (2 a + 4 b)
\][/tex]
4. Combine the like terms:
[tex]\[
a x - 2 b x + 2 a y + 4 b y
\][/tex]
After grouping, factoring, and simplifying where possible, we find that the simplified expression is:
[tex]\[
a x + 2 a y - 2 b x + 4 b y
\][/tex]
Thus, the expression simplifies to [tex]\( a x + 2 a y - 2 b x + 4 b y \)[/tex].
