Problem Analysis:
The task involves solving algebraic problems related to subtraction and addition of algebraic expressions. Let's go through each problem step by step.
---
Problem 1:
Subtract \(3p - 8q + 5r\) from \(7q + 10p - 3r\).
#### Solution:
1. Write the given expressions:
\[
\text{Expression 1: } 7q + 10p - 3r
\]
\[
\text{Expression 2: } 3p - 8q + 5r
\]
2. To subtract \(3p - 8q + 5r\) from \(7q + 10p - 3r\), we write:
\[
(7q + 10p - 3r) - (3p - 8q + 5r)
\]
3. Distribute the negative sign across the second expression:
\[
7q + 10p - 3r - 3p + 8q - 5r
\]
4. Combine like terms:
- For \(q\)-terms: \(7q + 8q = 15q\)
- For \(p\)-terms: \(10p - 3p = 7p\)
- For \(r\)-terms: \(-3r - 5r = -8r\)
5. Write the simplified expression:
\[
15q + 7p - 8r
\]
#### Final Answer for Problem 1:
\[
\boxed{15q + 7p - 8r}
\]
---
Problem 2:
Simplify \( (7a^3 + 3a^2 - 8a + 6) - (3a^3 - 2a^2 + 3a - 7) \).
#### Solution:
1. Write the given expressions:
\[
\text{Expression 1: } 7a^3 + 3a^2 - 8a + 6
\]
\[
\text{Expression 2: } 3a^3 - 2a^2 + 3a - 7
\]
2. To subtract \(3a^3 - 2a^2 + 3a - 7\) from \(7a^3 + 3a^2 - 8a + 6\), we write:
\[
(7a^3 + 3a^2 - 8a + 6) - (3a^3 - 2a^2 + 3a - 7)
\]
3. Distribute the negative sign across the second expression:
\[
7a^3 + 3a^2 - 8a + 6 - 3a^3 + 2a^2 - 3a + 7
\]
4. Combine like terms:
- For \(a^3\)-terms: \(7a^3 - 3a^3 = 4a^3\)
- For \(a^2\)-terms: \(3a^2 + 2a^2 = 5a^2\)
- For \(a\)-terms: \(-8a - 3a = -11a\)
- For constant terms: \(6 + 7 = 13\)
5. Write the simplified expression:
\[
4a^3 + 5a^2 - 11a + 13
\]
#### Final Answer for Problem 2:
\[
\boxed{4a^3 + 5a^2 - 11a + 13}
\]
---
Problem 3:
What should be added to \(2x - 3y + 5z\) to get \(7x - 3y + 2z\)?
#### Solution:
1. Let the expression to be added be \(A\). We need to find \(A\) such that:
\[
(2x - 3y + 5z) + A = 7x - 3y + 2z
\]
2. Rearrange to solve for \(A\):
\[
A = (7x - 3y + 2z) - (2x - 3y + 5z)
\]
3. Distribute the negative sign across the second expression:
\[
A = 7x - 3y + 2z - 2x + 3y - 5z
\]
4. Combine like terms:
- For \(x\)-terms: \(7x - 2x = 5x\)
- For \(y\)-terms: \(-3y + 3y = 0\)
- For \(z\)-terms: \(2z - 5z = -3z\)
5. Write the simplified expression for \(A\):
\[
A = 5x - 3z
\]
#### Final Answer for Problem 3:
\[
\boxed{5x - 3z}
\]
---
Summary of Answers:
1. \(15q + 7p - 8r\)
2. \(4a^3 + 5a^2 - 11a + 13\)
3. \(5x - 3z\)
Parent Tip: Review the logic above to help your child master the concept of addition of algebraic expressions worksheet.
