https://file.aiquickdraw.com/mathbot/file/1728725040004b346tgya.jpg

Let's work through some of the problems from your image. I'll start by solving the first few questions and provide detailed explanations.

### Problem 7: Simplify the expression
\[
a(b + c - bc) - b(c + a - ac) + c(b - a)
\]
We distribute the terms:
\[
a(b + c - bc) = ab + ac - abc
\]
\[
- b(c + a - ac) = -bc - ab + abc
\]
\[
c(b - a) = cb - ca = bc - ac
\]
Now, let's combine all the terms:
\[
ab + ac - abc - bc - ab + abc + bc - ac
\]
Notice that several terms cancel out:
\[
ab - ab + ac - ac - abc + abc - bc + bc = 0
\]
Thus, the simplified expression is **0**.

Answer: **E)**.

---

### Problem 8: If \( a + b + 3 = 10 \), find the value of:
\[
3a + 7, 7 + 1, 7b + 2, 5a + 11, 2 + 4, 6b
\]
First, solve \( a + b = 7 \) from \( a + b + 3 = 10 \).

Now, calculate the expressions one by one:
\[
3a + 7
\]
\[
7 + 1 = 8
\]
\[
7b + 2
\]
\[
5a + 11
\]
\[
2 +

Simplify the algebraic expressions and solve for values based on the given equations in the math problems, including simplifying terms, solving for variables, and finding specific values.

This page covers the simplification of algebraic expressions and solving for variable values, with step-by-step explanations. Topics include applying the distributive property and combining like terms. Suitable for Grades 8-10.

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