Question

___ should be added to ${9x}^2+18x$ to make it a perfect square.

• A. 9
• B. -9
• C. 7
• D. 4

Answer 1

The correct option is A

9

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

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

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

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

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

From (1) $a=3x$

Substituting value of a in (2),

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

$\Rightarrow b=3$

Therefore, $b^2$ is the term that needs to be added to it to make it perfect square.

Thus, we need to add 9.

Therefore, if we add 9 to ${9x}^2+18x$, it becomes

${9x}^2+18x+9=(3x+3{)}^2$

which is a perfect square.