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The factors of the expression $4 y 2 − 4 y + 1$ using appropriate identities is:

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(2y – 1) (y – 1)

(2y – 1) (2y – 1)

(2y – 1) (3y – 1)

(2y – 1) (4y – 1)

answer is B.

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Detailed Solution

Given:

4 y 2 − 4 y + 1

Let us rewrite the given expression as:

= (2 y) 2 − (2 × 2 y × 1) + 12

Comparing the given expression with a² - 2ab + b², we observe that a = 2y & b = 1.
By Using algebraic identity again, (a – b)² = a² – 2ab + b², we get:

4 y 2 − 4 y + 1 = (2 y − 1) 2

= (2 y − 1) (2 y − 1)

Hence, 4y² – 4y + 1 = (2y – 1) (2y – 1)
Therefore, the correct option is 2.

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