Question

Factorise the expression $(2a+b^2-4(2a+b\left)\right)$ + 3.

• A. (2a+b-3)(2a+b-1)
  
• B. (2a+b-3)(2a-b-1)
  
• C. (2a-b-3)(2a+b-1)
  
• D. (2a+b+3)(2a+b-1)
  

Answer 1

The correct option is A (2a+b-3)(2a+b-1)


The given expression is $(2a+b{)}^2-4(2a+b)+3$
Taking 2a + b = x, the expression reduces to
$x^2-4x+3$
The product of first and last term is $3x^2$
The middle term is -4x
So, two terms whose product is $3x^2$ and sum is $-4x$ will be
$-3xand-x$
So, splitting the middle term we get,
= $x^2-x-3x+3$
= $x(x-1)-3(x-1)$
= $(x-3)(x-1)$ [Taking (x-1) common]
Substituting back the value of x we get
$(2a+b-3)(2a+b-1)$