This is level 4: completely factorising an expression of two parts that can be separately factorised. You can earn a trophy if you get at least 9 questions correct.

Order the terms in your answers in the same order as they appear in the question.

3a+6ab+20w+15wy

2cd−4c+6w−4wy

10bf+25bg−21p−14pq

3a²+2ab+7w−28wy

d²−11d+9ef+12e²

8m²−2mn+4p²q+16pq²

Let's work through completely factorizing each expression as per Level 4 instructions.

### 1. \( 3a + 6ab + 20w + 15wy \)
- Factor each part:
  - \( 3a + 6ab = 3a(1 + 2b) \)
  - \( 20w + 15wy = 5w(4 + 3y) \)
  
  **Final Factorized Form**:  
  \[ 3a(1 + 2b) + 5w(4 + 3y) \]

### 2. \( 2cd − 4c + 6w − 4wy \)
- Factor each part:
  - \( 2cd - 4c = 2c(d - 2) \)
  - \( 6w - 4wy = 2w(3 - 2y) \)
  
  **Final Factorized Form**:  
  \[ 2c(d - 2) + 2w(3 - 2y) \]

### 3. \( 10bf + 25bg − 21p − 14pq \)
- Factor each part:
  - \( 10bf + 25bg = 5b(2f + 5g) \)
  - \( -21p - 14pq = -7p(3 + 2q) \)
  
  **Final Factorized Form**:  
  \[ 5b(2f + 5g) - 7p(3 + 2q) \]

### 4. \( 3a² + 2ab + 7w − 28wy \)
- Factor each part:
  - \( 3a² + 2ab = a(3a + 2b) \)
  - \( 7w - 28wy = 7w(1 - 4y) \)
  
  **Final Factorized Form**:  
  \[ a(3a + 2b) + 7w(1 - 4y) \]

### 5. \( d² − 11d + 9ef + 12e² \)
- Factor each part:
  - \( d² - 11d = d(d - 11) \)
  - \( 9ef + 12e² = 3e(3f + 4e) \)
  
  **Final Factorized Form**:  
  \[ d(d - 11) + 3e(3f + 4e) \]

### 6. \( 8m² − 2mn + 4p²q + 16pq² \)
- Factor each part:
  - \( 8m² - 2mn = 2m(4m - n) \)
  - \( 4p²q + 16pq² = 4pq(p + 4q) \)
  
  **Final Factorized Form**:  
  \[ 2m(4m - n) + 4pq(p + 4q) \]

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Feel free to ask for more details on any step!

**Expansion Questions**:
1. What are the steps to factor a quadratic expression?
2. How can you identify common factors in an expression?
3. Why is grouping useful in factorizing more complex expressions?
4. What methods can be used if terms do not have common factors?
5. Can you explain the difference between factoring and expanding?

**Tip**: Always start by factoring out the greatest common factor (GCF) from each part of the expression!

This is level 4: completely factorising an expression of two parts that can be separately factorised. You can earn a trophy if you get at least 9 questions correct.

3a+6ab+20w+15wy

2cd−4c+6w−4wy

10bf+25bg−21p−14pq

3a²+2ab+7w−28wy

d²−11d+9ef+12e²

8m²−2mn+4p²q+16pq²

Master the skill of completely factorizing complex algebraic expressions involving two parts. This advanced Level 4 guide covers key algebraic concepts, including factoring by grouping and using the Greatest Common Factor (GCF). Suitable for students in Grades 8-10 looking to sharpen their factoring skills.

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