Sure! Let's simplify each expression by combining like terms.
### a) Simplify the expression [tex]\(2a + b + a - 3b\)[/tex]
1. Identify like terms:
- Terms involving [tex]\(a\)[/tex]: [tex]\(2a\)[/tex] and [tex]\(a\)[/tex].
- Terms involving [tex]\(b\)[/tex]: [tex]\(b\)[/tex] and [tex]\(-3b\)[/tex].
2. Combine like terms:
- Combine terms with [tex]\(a\)[/tex]: [tex]\(2a + a = 3a\)[/tex].
- Combine terms with [tex]\(b\)[/tex]: [tex]\(b - 3b = -2b\)[/tex].
3. Write the simplified expression:
[tex]\[
2a + b + a - 3b = 3a - 2b
\][/tex]
### b) Simplify the expression [tex]\(x + 3y + 2x - 4y\)[/tex]
1. Identify like terms:
- Terms involving [tex]\(x\)[/tex]: [tex]\(x\)[/tex] and [tex]\(2x\)[/tex].
- Terms involving [tex]\(y\)[/tex]: [tex]\(3y\)[/tex] and [tex]\(-4y\)[/tex].
2. Combine like terms:
- Combine terms with [tex]\(x\)[/tex]: [tex]\(x + 2x = 3x\)[/tex].
- Combine terms with [tex]\(y\)[/tex]: [tex]\(3y - 4y = -y\)[/tex].
3. Write the simplified expression:
[tex]\[
x + 3y + 2x - 4y = 3x - y
\][/tex]
### c) Simplify the expression [tex]\(f + 2g - 3f + g + f - 5\)[/tex]
1. Identify like terms:
- Terms involving [tex]\(f\)[/tex]: [tex]\(f\)[/tex], [tex]\(-3f\)[/tex], and [tex]\(f\)[/tex].
- Terms involving [tex]\(g\)[/tex]: [tex]\(2g\)[/tex] and [tex]\(g\)[/tex].
- Constant term: [tex]\(-5\)[/tex].
2. Combine like terms:
- Combine terms with [tex]\(f\)[/tex]: [tex]\(f - 3f + f = -f\)[/tex].
- Combine terms with [tex]\(g\)[/tex]: [tex]\(2g + g = 3g\)[/tex].
- The constant term remains [tex]\(-5\)[/tex].
3. Write the simplified expression:
[tex]\[
f + 2g - 3f + g + f - 5 = -f + 3g - 5
\][/tex]
### Final Answers:
1. [tex]\(2a + b + a - 3b = 3a - 2b\)[/tex]
2. [tex]\(x + 3y + 2x - 4y = 3x - y\)[/tex]
3. [tex]\(f + 2g - 3f + g + f - 5 = -f + 3g - 5\)[/tex]
These are the simplified expressions after rearranging and combining like terms.
