Question

Solve $(ab+1{)}^2$ - $(ab{)}^2$ where, b - a = 1.

• A. $a^2$ + $b^2$
• B. $a^2$ + $(b+1{)}^2$
• C. $(a+1{)}^2$ + $(b+1{)}^2$
• D. $b^2$

Answer 1

The correct option is A $a^2$ + $b^2$

$(ab+1{)}^2-(ab{)}^2=\left(a\right(a+1)+1{)}^2-(a(a+1){)}^2$
$=\left(a^2\right(a+1{)}^2+1+2a(a+1))-\left(a^2\right(a+1{)}^2)$
$=2a(a+1)+1$
$=2a^2+2a+1$
$=a^2+2a+1+a^2$
$=(a+1{)}^2+a^2$
$=b^2+a^2$ [since $b=a+1$]