https://r2.erweima.ai/mathbot/image/17259203663933g1ctbwx.jpg

Let's go through the problems in the image one by one.

### Problem 4:
\[
8(p - 9) + (9 - p)^2
\]

**Step 1:** Distribute the \( 8 \) in the first term:
\[
8p - 72 + (9 - p)^2
\]

**Step 2:** Expand \( (9 - p)^2 \):
\[
(9 - p)^2 = (9 - p)(9 - p) = 81 - 18p + p^2
\]

**Step 3:** Combine everything:
\[
8p - 72 + 81 - 18p + p^2
\]

**Step 4:** Combine like terms:
\[
p^2 - 10p + 9
\]

### Problem 5:
\[
3a^2 - 10b - 6ab + 5a
\]

This is a simplified polynomial expression, and since no common terms exist to combine, it stays as it is:
\[
3a^2 - 6ab + 5a - 10b
\]

### Problem 6:
\[
-12 + 36x^3 - 9x^2 + 48x
\]

**Step 1:** Look for common factors. The greatest common factor (GCF) of all terms is \(3\).

**Step 2:** Factor out \(3\):
\[
3(-4 + 12x^3 - 3x^2 + 16x)
\]

Alternatively, if factoring by \(12\) (which would divide all terms except the first), you can factor smaller but maintain more simplicity.

Would you like any further details on these problems?

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Here are 5 related questions to practice:
1. Expand and simplify: \((2p - 3)^2 + 4(p + 1)\)
2. Factor: \(6x^2 - 18x + 12\)
3. Simplify: \(4a^2b - 6ab + 2a\)
4. Expand: \((p + 5)(p - 7)\)
5. Factor: \(9x^3 - 27x^2 + 18x\)

**Tip:** Always check for common factors in every term before expanding or simplifying further.

Solve the following algebraic expressions:
4. 8(p - 9) + (9 - p)^2
5. 3a^2 - 10b - 6ab + 5a
6. -12 + 36x^3 - 9x^2 + 48x

This solution covers the simplification of algebraic expressions, including polynomial expansions, factoring, and the use of common formulas. Problems involve factoring and simplifying expressions like 8(p - 9) + (9 - p)^2 and 36x^3 - 9x^2 + 48x. Ideal for students in Grades 8-10.

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