## Answer :

### 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.