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Let's start by addressing the questions visible in the image:

### Question 4: Using identities, factorise the following:
(a) \( 36m^2 - 81n^2 \)  
(b) \( 50x^2 - 98y^2 \)  
(c) \( 16z^2 - 9y^2 \)  
(d) \( 25x^2 - 90xy + 81y^2 \)  
(e) \( 121x^2 - 88xy + 16y^2 \)

#### Solutions:
1. **(a) \( 36m^2 - 81n^2 \)**:  
   This is a difference of squares:  
   \[
   36m^2 - 81n^2 = (6m - 9n)(6m + 9n)
   \]

2. **(b) \( 50x^2 - 98y^2 \)**:  
   Factor out the common factor 2:  
   \[
   50x^2 - 98y^2 = 2(25x^2 - 49y^2) = 2(5x - 7y)(5x + 7y)
   \]

3. **(c) \( 16z^2 - 9y^2 \)**:  
   This is a difference of squares:  
   \[
   16z^2 - 9y^2 = (4z - 3y)(4z + 3y)
   \]

4. **(d) \( 25x^2 - 90xy + 81y^2 \)**:  
   This is a perfect square trinomial:  
   \[
   25x^2 - 90xy + 81y^2 = (5x - 9y)^2
   \]

5. **(e) \( 121x^2 - 88xy + 16y^2 \)**:  
   This is also a perfect square trinomial:  
   \[
   121x^2 - 88xy + 16y^2 = (11x - 4y)^2
   \]

Would you like further clarifications or details on any of these steps?

### Relative Questions:
1. What is the method for factoring difference of squares in general?
2. How can you recognize a perfect square trinomial?
3. What happens if one of the terms in a trinomial doesn't perfectly match the conditions for being a perfect square?
4. Can the process of factoring be applied to all polynomials? Why or why not?
5. How does factoring help in solving quadratic equations?

### Tip:
When factorizing, always check for common factors first before applying more complex techniques like difference of squares or trinomial factoring.

Factorise the given algebraic expressions using identities, factorisation techniques, and the method of dividing expressions.

Learn how to factor algebraic expressions like 36m^2 - 81n^2 and 50x^2 - 98y^2 using difference of squares and trinomial identities. Detailed step-by-step solutions for Grade 8 students.

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