Question

What number should be added to ${9x}^2$ + 18 $x$ to make it a perfect square?

Answer 1

Let us compare ${9x}^2$ + 18 $x$ with expansion of ${(a+b)}^2$.

$(a+b{)}^2$=$a^2$+ 2ab + $b^2$

On comparing terms of RHS of above equation and 9$x^2$+ 18$x$, it is clear that-

$a^2$= 9$x^2$ .... (1)

18$x$ = 2ab .... (2)

From (1) a = 3$x$

Substituting value of a in (2),

18$x$= 2(3$x$)b

b = 3

In given question that the constant term $b^2$ is what is missing from given equation and needs to be added to it to make it perfect square.

Thus, we need to add 9.