Certainly! Let's factorize the expression [tex]\(2ax + 4ay - 3bx - 6by\)[/tex] step by step.
1. Identify Common Factors:
- In the terms [tex]\(2ax + 4ay\)[/tex], both [tex]\(2ax\)[/tex] and [tex]\(4ay\)[/tex] share a common factor of [tex]\(2a\)[/tex].
- In the terms [tex]\(-3bx - 6by\)[/tex], both [tex]\(-3bx\)[/tex] and [tex]\(-6by\)[/tex] share a common factor of [tex]\(-3b\)[/tex].
2. Factor Out Common Factors in Pairs:
- For [tex]\(2ax + 4ay\)[/tex]:
[tex]\[
2ax + 4ay = 2a(x + 2y)
\][/tex]
- For [tex]\(-3bx - 6by\)[/tex]:
[tex]\[
-3bx - 6by = -3b(x + 2y)
\][/tex]
3. Combine the Factored Terms:
- Notice that both groups now share a common binomial factor [tex]\((x + 2y)\)[/tex]:
[tex]\[
2a(x + 2y) - 3b(x + 2y)
\][/tex]
4. Factor Out the Common Binomial:
- Factor out [tex]\((x + 2y)\)[/tex] from the entire expression:
[tex]\[
2a(x + 2y) - 3b(x + 2y) = (x + 2y)(2a - 3b)
\][/tex]
So, the fully factored form of the expression [tex]\(2ax + 4ay - 3bx - 6by\)[/tex] is:
[tex]\[
(x + 2y)(2a - 3b)
\][/tex]
