Question

Which of the following is the factor of 4a² + b²- 4ab + 2b - 4a + 1 (A) (a - b) (B) (a + b-2) (C) (a - b +2) (D) (2a - 6-1)​

Answer 1

Answer:

Option (D) is correct

Step-by-step explanation:

4a²+b²-4ab+2b-4a+1

= [(2a)²+b²-2×2a×b]+2(b-2a)+1

= (2a-b)²+2(b-2a)+1

= (2a-b)²-2×(2a-b)×1+1²

= (2a-b-1)²

= (2a-b-1)(2a-b-1)

Therefore,

Option (D) is correct

•••♪

Answer 2

The factor of 4a² + b²- 4ab + 2b - 4a + 1 is:

(D) (2a - 6-1)​

Step-by-step explanation:

4a² + b²- 4ab + 2b - 4a + 1

Grouping the given expressions:

(4a² + b²- 4ab) + 2b - 4a + 1

((2a)² + (b)²- (4ab)) + 2b - 4a + 1

((2a)² + (b)²- (2×2a×b)) + 2b - 4a + 1

Applying the formula: a² + b² -2ab = (a-b)²

(2a-b)² + 2b - 4a + 1

Taking -2 as common:

(2a-b)² -2 (-b + 2a) + 1

(2a-b)² -2 (2a - b) + 1

(2a-b)² -2 (2a - b) + (1)²

Applying the formula: a² + b² -2ab = (a-b)²

(2a - b - 1)²

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