To answer Exercise 9.5 Question 3 of Maths Class 8, we need to understand the concepts of algebraic expressions and identities. Let's break down the question and explain it step by step.

Question:
If (a + b)² = 16 and ab = 6, find the value of (a - b)².

Solution:

Step 1: Understanding the given information
The given information states that (a + b)² equals 16, and the value of ab is 6. We need to find the value of (a - b)².

Step 2: Expanding (a + b)²
To solve this problem, we need to expand the expression (a + b)². This can be done using the formula:

(a + b)² = a² + 2ab + b²

Step 3: Substituting the given values
Now, let's substitute the given information into the formula. Since (a + b)² equals 16, we can write:

16 = a² + 2ab + b²

Similarly, we know that ab equals 6, so we substitute this value as well:

16 = a² + 2(6) + b²

Simplifying further:

16 = a² + 12 + b²

Step 4: Rearranging the equation
To find the value of (a - b)², we need to manipulate the equation. Let's rearrange the equation by subtracting 16 from both sides:

a² + b² + 12 - 16 = 0

Simplifying further:

a² + b² - 4 = 0

Step 5: Recognizing a special identity
The equation a² + b² - 4 = 0 represents a special identity. It is the identity for the square of the difference of two terms:

(a - b)² = a² + b² - 2ab

Comparing this identity with the equation we obtained:

(a - b)² = a² + b² - 2ab

We can see that the value of 2ab is missing in our equation. However, we know that ab equals 6 from the given information. So, let's substitute this value:

(a - b)² = a² + b² - 2(6)

Simplifying further:

(a - b)² = a² + b² - 12

Step 6: Evaluating (a - b)²
We have successfully rearranged the equation and substituted the values. Now, we can evaluate (a - b)² by substituting the values of a², b², and 12:

(a - b)² = 16 - 12

Simplifying further:

(a - b)² = 4

Step 7: Final Answer
Therefore, the value of (a - b)² is 4.

To summarize:
- The given equation is (a + b)² = 16 and ab = 6.
- By expanding (a + b)², we get a² + 2ab + b².
- Substituting the given values, we have

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