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Mathematics

a2 + 2a + 1 - b2 - x2 + 2bx is equal to :

  1. (a + 1 - b + x) (a - 1 - b + x)

  2. (a + 1 + b - x) (a + 1 - b + x)

  3. (a - 1 + b - x) (a - 1 - b + x)

  4. (a - 1 + bx) (a + 1 - bx)

Factorisation

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Answer

a2 + 2a + 1 - b2 - x2 + 2bx

Using the formula

[∵ (x - y)2 = x2- 2xy + y2 ]

And

[∵ (x + y)2 = x2+ 2xy + y2 ]

= (a2 + 2a + 1) - (b2 + x2 - 2bx)

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

Using the formula

[∵ (x2 - y2) = (x + y)(x - y)]

= ((a + 1) + (b - x))((a + 1) - (b - x))

= (a + 1 + b - x)(a + 1 - b + x)

Hence, option 2 is the correct option.

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