Question

If $(mn-1{)}^2=(mn{)}^2+1+2y$, then y is equal to

• A. $mn$
• B. $m$
• C. $-2m$
• D. $-mn$

Answer 1

The correct option is D $-mn$

We know, $(x-y{)}^2=x^2-2xy+y^2$.
Expanding $(mn-1{)}^2$ using the above identity, we get,
$(mn-1{)}^2=(mn{)}^2-2\left(mn\right)\left(1\right)+(1{)}^2$
$=(mn{)}^2-2mn+1$
$=(mn{)}^2+1+2(-mn)$
So, $(mn-1{)}^2=(mn{)}^2+1+2(-mn)$ --- (1)
Given, $(mn-1{)}^2=(mn{)}^2+1+2y$ --- (2)
Comparing (1) and (2), we get, y = -mn.