Question

Q.Factorise the following using appropriate identity.
${4y}^{2} - 4y + 1$

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Answer 1

Method 1:

Given quadratic expression:

4y²-4y+1

= (2y)²-2×2y×1+1²

=(2y-1)²

_______________________

By algebraic identity:

a²-2ab+b² = (a-b)²

_______________________

= (2y-1)(2y-1)

Therefore,

4y²-4y+1 = (2y-1)(2y-1)

Method 2:

4y²-4y+1

Splitting the middle term, we get

= 4y² - 2y -2y +1

= 2y(2y-1)-1(2y-1)

= (2y-1)(2y-1)

Therefore,

4y²-4y+1 = (2y-1)(2y-1)

Answer 2

Step-by-step explanation:

1 can be written as 1^2

(4y)^2-4y+1^2 #identity: (a-b)^2=a^2+b^2-2ab#

(4y)^2-2*2y*1+1^2

so, (4y-1)^2

(4y-1)(4y-1)