Question

$(a +b) {}^{2} - 1$
Factorise the following

Answer 1

Solution -  

​​(a + b)² - 1  

= (a + b)² - (1)²  

= (a + b + 1) (a + b - 1)    

Answer : (a + b + 1) (a + b - 1)  

Explaination -

Identity used : a² - b² = (a + b) (a - b)    

We know,  ​

1 is an exceptional number as 1² = 1

(1×1 = 1)  

So, we can write 1 as 1²  

By using identity    

a² - b² = (a + b) (a - b)  

Where,  

a² = (a + b)²  

b² = (1)²  

So,  

a² - b² = (a + b)² - (1)²​​

= (a + b) (a - b) = (a + b + 1) (a + b - 1)

∴ The Answer is (a + b + 1) (a + b - 1)

#Be Brainly

Answer 2

${(a + b)}^{2} - 1 \\ \\ = {(a + b)}^{2} - {1}^{2} \\ \\ = (a + b + 1)(a + b - 1)$