Question

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

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$x$,

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

$18x=2ab$ .... (2) [1 Mark]

From (1) $a=3x$

Substituting value of $a$ in (2),

$18x=2\left(3\right)\left(x\right)b$

$b=3\Rightarrow b^2=9$
Thus, we need to add 9. [1 Mark]