From the image provided, the worksheet includes questions about expanding brackets, simplifying expressions, and fully factorizing given expressions. I will review the solutions presented and provide clarifications or corrections where needed.

Analysis and Corrections

Q1: Expand the brackets and simplify

(a) $3x^2(2x - 5)(4 - x)$

• The work appears to involve distribution. Let's recheck:
  1. Expand $(2x - 5)(4 - x)$:
     $(2x - 5)(4 - x) = 8x - 2x^2 - 20 + 5x = -2x^2 + 13x - 20$.
  2. Multiply by $3x^2$:
     $3x^2(-2x^2 + 13x - 20) = -6x^4 + 39x^3 - 60x^2$.

Final simplified answer: $-6x^4 + 39x^3 - 60x^2$

(b) $2x^2 - (x + 3)(2 - x)$

• First, expand $(x + 3)(2 - x)$:
  $= 2x - x^2 + 6 - 3x = -x^2 - x + 6$.
• Subtract from $2x^2$:
  $2x^2 - (-x^2 - x + 6) = 2x^2 + x^2 + x - 6 = 3x^2 + x - 6$.

Final simplified answer: $3x^2 + x - 6$

Q2: Fully factorize

(a) $50x^2 - 32y^2$

• This is a difference of squares: $50x^2 - 32y^2 = 2(25x^2 - 16y^2) = 2(5x - 4y)(5x + 4y)$

(b) $5x^2 - 9x + 4$

• Factorize by splitting the middle term:
  1. Find two numbers that multiply to $5 \times 4 = 20$ and add to $-9$: $-5$ and $-4$.
  2. Rewrite:
     $5x^2 - 5x - 4x + 4 = 5x(x - 1) - 4(x - 1) = (5x - 4)(x - 1)$.

Final factorized form: $(5x - 4)(x - 1)$

Summary of Errors

1. For Q1(a), there was a partial miscalculation in combining terms, and the final expanded form was incorrect.
2. For Q1(b), the subtraction of $(x + 3)(2 - x)$ wasn't fully simplified.
3. For Q2(b), the factoring method was inconsistent with the final expression.

Would you like more details on any of the steps?
Here are 5 follow-up questions to deepen understanding:

1. How do you identify and simplify terms when expanding brackets in algebraic expressions?
2. What is the significance of the difference of squares in factorization?
3. How can you ensure accuracy when distributing negative signs?
4. Can you use alternative methods to factorize quadratic equations, such as completing the square?
5. How do you verify if your expanded or factorized expressions are correct?

Tip: Always double-check your work by re-expanding your factorized form to match the original expression.