Question

factorise (2a + b)^2+ 3(2a + b) + 2​

Answer 1

Step-by-step explanation:

Given :-

(2a + b)²+ 3(2a + b) + 2

To find :-

Factorize the expression ?

Solution :-

Method -1:-

Given expression is (2a + b)²+3(2a + b)+ 2

=> (2a+b)²+(2a+b)+2(2a+b)² +2

=> (2a+b)(2a+b+1)+2(2a+b+1)

=> (2a+b+1)(2a+b+2)

Method-2:-

Given expression is (2a + b)²+ 3(2a + b)+ 2

Put 2a+b = x then

=> x²+3x+2

=> x²+x+2x+2

=> x(x+1)+2(x+1)

=> (x+1)(x+2)

=> (2a+b+1)(2a+b+2)

Answer:-

(2a + b)²+ 3(2a + b) + 2 =(2a+b+1)(2a+b+2)

Used Method :-

→ Splitting the middle term