https://file.aiquickdraw.com/mathbot/file/1728308007564ajdzejqs.jpg

Let’s go through each expression one by one and simplify them.

### Expression c:
\[
5(r + 2s) + 3(r + s)
\]
Expanding the terms:
\[
= 5r + 10s + 3r + 3s = (5r + 3r) + (10s + 3s) = 8r + 13s
\]

### Expression d:
\[
3(2r - 2s) + 4(r + 3s)
\]
Expanding the terms:
\[
= 6r - 6s + 4r + 12s = (6r + 4r) + (-6s + 12s) = 10r + 6s
\]

### Expression e:
\[
7(q - 4p) + 6(2q + 5p)
\]
Expanding the terms:
\[
= 7q - 28p + 12q + 30p = (7q + 12q) + (-28p + 30p) = 19q + 2p
\]

### Expression f:
\[
4(3x - 4p) + 6(2q + 5p)
\]
Expanding the terms:
\[
= 12x - 16p + 12q + 30p = 12x + 12q + (-16p + 30p) = 12x + 12q + 14p
\]

### Expression g:
\[
7(3 - 2z) + 3(2z - 2)
\]
Expanding the terms:
\[
= 21 - 14z + 6z - 6 = -8z + 15
\]

### Expression h:
\[
14 + 3(y + 4) - 2y
\]
Expanding the terms:
\[
= 14 + 3y + 12 - 2y = (3y - 2y) + (14 + 12) = y + 26
\]

### Expression i:
\[
7p + 6(4 - 2p) - 7
\]
Expanding the terms:
\[
= 7p + 24 - 12p - 7 = (7p - 12p) + (24 - 7) = -5p + 17
\]

### Summary of Simplified Expressions:
1. **c:** \( 8r + 13s \)
2. **d:** \( 10r + 6s \)
3. **e:** \( 19q + 2p \)
4. **f:** \( 12x + 12q + 14p \)
5. **g:** \( -8z + 15 \)
6. **h:** \( y + 26 \)
7. **i:** \( -5p + 17 \)

Would you like further details on any specific part of the simplification process?

---

Here are some related questions to explore:
1. What is the distributive property and why is it useful in simplifying expressions?
2. How would these expressions change if you added an additional term inside each parenthesis?
3. What are common mistakes to watch for when distributing terms over addition and subtraction?
4. How can combining like terms simplify the process of solving equations?
5. In what scenarios might we need to re-factor the simplified expressions?

**Tip:** When simplifying expressions, double-check each step, especially when distributing negative signs or coefficients to ensure accuracy.

Learn how to simplify algebraic expressions step by step using the distributive property. This problem covers key concepts such as combining like terms and the application of the distributive property. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation