To solve the problem of finding the difference between the two expressions [tex]\(4x + 9y\)[/tex] and [tex]\(3x + 6y\)[/tex], follow these steps:
1. Write down the expressions:
- The first expression is [tex]\(4x + 9y\)[/tex].
- The second expression is [tex]\(3x + 6y\)[/tex].
2. Subtract the second expression from the first expression:
[tex]\[
(4x + 9y) - (3x + 6y)
\][/tex]
3. Distribute the subtraction:
[tex]\[
4x + 9y - 3x - 6y
\][/tex]
4. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(4x - 3x = x\)[/tex].
- Combine the [tex]\(y\)[/tex] terms: [tex]\(9y - 6y = 3y\)[/tex].
5. Write down the simplified expression:
[tex]\[
x + 3y
\][/tex]
Therefore, the expression that represents the difference between [tex]\(4x + 9y\)[/tex] and [tex]\(3x + 6y\)[/tex] in its simplest form is [tex]\(x + 3y\)[/tex].
