Question

Factorise: 4 2-4 x + 1

Answer 1

Factorise : 4x

2

+4x+1

Given: 4x

2

+4x+1

=4x

2

+2x+2x+1, (split middle term so that resultant is same)

=(4x

2

+2x)+(2x+1), (group pair of terms)

=2x(2x+1)+1(2x+1), (factor each binomials)

=(2x+1)(2x+1), (factor out common factor (2x+1))

=(2x+1)

2

Aliter, use (a+b

2

)=a

2

+2ab+b

2

⇒4x

2

+4x+1=(2x)

2

+2×2x+1

2

=(2x+1)

2