Question

Read the question in the picture .

Answer 1

Answer- The above question is from the chapter 'Algebraic Expressions'.

Important identities:

1) (a+b)² = a² + 2ab + b²

2) (a-b)² = a² - 2ab + b²

3) (a+b) (a-b)= a² - b²

 

Let's take an example of (2+3) (2-3).

This is in the form (a+b) (a-b) where a= 2 and b= 3.

By using identity of (a+b) (a-b)= a² - b²,

(2+3) (2-3)

= 2² - 3²

= 4 - 9                  

= -5  

If we check this by simple calculation,

(2+3) (2-3)= 5 × -1 = -5  

Given question: Factorise x² - 81 using the difference of two squares.

a) (x - 81) (x + 81)

b) (x - 9) (x - 9)

c) (x + 9) (x - 9)

d) (x + 9) (x + 9)  

Solution: This is in the form a² - b², where a= x and b= 9. By using identity of (a+b) (a-b)= a² - b²,

x² - 81  

= (x + 9) (x - 9)  

∴ (c) (x + 9) (x - 9) is the correct answer.