The worksheet appears to involve simplifying algebraic expressions by combining like terms and using the distributive property. Let's break it down step-by-step:

Problems & Solutions:

1. (a) $4x + 3 + 2x + 1$
   • Combine like terms:
     • $4x + 2x = 6x$
     • $3 + 1 = 4$
   • Final answer: $6x + 4$

2. (b) $3a + 2b + 8a + 4$
   • Combine like terms:
     • $3a + 8a = 11a$
     • $2b = 2b$ (no terms to combine with)
     • $4 = 4$
   • Final answer: $11a + 2b + 4$

3. (c) $8c + 2b + 3b + 6$
   • Combine like terms:
     • $8c = 8c$ (no terms to combine with)
     • $2b + 3b = 5b$
     • $6 = 6$
   • Final answer: $8c + 5b + 6$

4. (d) $10 + 6y + 2x + 3$
   • Combine like terms:
     • $10 + 3 = 13$
     • $6y = 6y$ (no terms to combine with)
     • $2x = 2x$ (no terms to combine with)
   • Final answer: $2x + 6y + 13$

5. (e) $4c + 2 + c + 1$
   • Combine like terms:
     • $4c + c = 5c$
     • $2 + 1 = 3$
   • Final answer: $5c + 3$

6. (f) $3x + 2y + 7 + 2x$
   • Combine like terms:
     • $3x + 2x = 5x$
     • $2y = 2y$ (no terms to combine with)
     • $7 = 7$
   • Final answer: $5x + 2y + 7$

7. (g) $2(6h + 8)$
   • Use the distributive property:
     • $2 \cdot 6h = 12h$
     • $2 \cdot 8 = 16$
   • Final answer: $12h + 16$

8. (h) $6(5e + 6)$
   • Use the distributive property:
     • $6 \cdot 5e = 30e$
     • $6 \cdot 6 = 36$
   • Final answer: $30e + 36$

9. (i) $7(3g + 10)$
   • Use the distributive property:
     • $7 \cdot 3g = 21g$
     • $7 \cdot 10 = 70$
   • Final answer: $21g + 70$

10. (j) $11(4d + 8)$
    • Use the distributive property:
      • $11 \cdot 4d = 44d$
      • $11 \cdot 8 = 88$
    • Final answer: $44d + 88$

Let me know if you want any step clarified! 😊

5 Related Questions:

1. What are "like terms," and why do we combine them?
2. How does the distributive property work, and where is it used in real-life applications?
3. How would you simplify an expression like $4(a + b) + 3a - 2b$?
4. If $x = 2$, $y = 3$, and $z = 4$, how would you evaluate $3x + 5y - z$?
5. What happens when we distribute negative coefficients, such as $-2(3x - 4)$?

Tip:

When simplifying expressions, always group and combine like terms first before applying other properties, like distribution. This ensures clarity and avoids mistakes.