Let’s solve the questions step by step. I will explain each part clearly:

6a) $a + (a - b)$

Combine like terms: $a + a - b = 2a - b$

6b) $5a^2 - a^2$

Simplify the terms: $5a^2 - a^2 = 4a^2$

6c) $3z^2 - 4z^2$

Simplify the terms: $3z^2 - 4z^2 = -z^2$

7a) $a(a - b)$

Distribute $a$: $a(a - b) = a^2 - ab$

7b) $2x(2x + 3)$

Distribute $2x$: $2x(2x + 3) = 4x^2 + 6x$

7c) $3(2a^2 - 1) + 3$

Distribute $3$ and simplify: $3(2a^2 - 1) + 3 = 6a^2 - 3 + 3 = 6a^2$

8a) $\frac{3y + 2y}{5}$

Combine terms in the numerator: $\frac{3y + 2y}{5} = \frac{5y}{5} = y$

8b) $3xy - x(y + 1)$

Distribute $x$ and simplify: $3xy - x(y + 1) = 3xy - xy - x = 2xy - x$

8c) $2 + \frac{2a - a}{a}$

Simplify the fraction: $\frac{2a - a}{a} = \frac{a}{a} = 1$ Now add: $2 + 1 = 3$

Let me know if you need detailed explanations for any of these steps!

5 Related Questions

1. How can we combine like terms in algebraic expressions?
2. What are the rules for distributing terms in parentheses?
3. How do we simplify fractions with algebraic numerators and denominators?
4. What are common errors to avoid when expanding expressions?
5. How do coefficients affect combining like terms?

Tip:

Always double-check your work for signs (positive/negative) when simplifying expressions!