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The worksheet focuses on simple factorization, particularly reviewing how to factor algebraic expressions by taking out common factors and using methods like grouping terms.

Let's work through the provided problems:

### Problem 1
\[ 50p^2q + 35p^3q^2 \]

Factor out the greatest common factor (GCF), which is \( 5p \):
\[
5p(10q + 7p^2q^2)
\]

### Problem 2
\[ 12a^3 - 3a^2(a + 2) \]

Start by factoring out the GCF, which is \( 3a^2 \):
\[
3a^2(4 - (a + 2)) = 3a^2(4 - a - 2)
= 3a^2(2 - a)
\]

### Problem 3
\[ 5(a - 3) - 2u(3 - a) \]

Notice that \( 3 - a \) can be rewritten as \( -(a - 3) \):
\[
5(a - 3) + 2u(a - 3) = (a - 3)(5 + 2u)
\]

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

Use the fact that \( 9 - p = -(p - 9) \):
\[
8(p - 9) + (-(p - 9))^2 = 8(p - 9) + (p - 9)^2
= (p - 9)(8 + (p - 9))
\]
\[
= (p - 9)(p - 1)
\]

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

Group the terms:
\[
(3a^2 + 5a) - (6ab + 10b)
\]
Factor:
\[
a(3a + 5) - 2b(3a + 5)
\]
Factor out \( (3a + 5) \):
\[
(3a + 5)(a - 2b)
\]

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

Factor out \( -3 \):
\[
-3(4 - 12x^3 + 3x^2 - 16x)
\]
Factor further, grouping terms or simplifying.

Let me know if you'd like further details on any problem!

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Here are five related questions to expand your understanding:
1. How do you identify the greatest common factor in an expression?
2. How can you factor trinomials using grouping methods?
3. What is the importance of factoring before solving algebraic equations?
4. Can all expressions be factored using the difference of squares?
5. How do you handle expressions that involve higher powers, like \( x^3 \)?

**Tip:** Always look for common factors first to simplify the factorization process.

Factor the following algebraic expressions: 50p^2q + 35p^3q^2, 12a^3 - 3a^2(a + 2), 5(a - 3) - 2u(3 - a), 8(p - 9) + (9 - p)^2, 3a^2 - 10b - 6ab + 5a, -12 + 36x^3 - 9x^2 + 48x.

Explore algebraic factorization problems including common factors and grouping techniques. This worksheet provides detailed steps to factor expressions such as 50p^2q + 35p^3q^2, 12a^3 - 3a^2(a + 2), and more. Suitable for students in Grades 8-10.

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