Question

Please answer this question

Answer 1

Question :-

♣ 1 + 2ab - (a² + b²) is equal to

Solution :-

The given expression is

1 + 2ab - (a² + b²)

Now, the above expression can be written as,

$\rm{1 - (a {}^{2} + b {}^{2} - 2ab) }$

The above expression can be written as

$\rm{1 - (a - b) {}^{2} \: \: \: \{ \because (a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab} \}$

Now we get,

$\rm{ (1) {}^{2} - (a - b) {}^{2} \: \: \{ \because since \: 1 = 1 {}^{2} \} }$

Now, on expanding the above equation, the new expression is,

$\small\rm{[1 + (a - b ) ] [ 1 - (a-b) ] } \: \: \{\because(a + b)(a - b) = a {}^{2} - b {}^{2} \}$

The equation becomes,

$\rm{(1 + a - b)(1 - a + b})$

Hence, Option (B) is the right answer.

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