Question

If is added to $x^2+8x$, it will become a perfect square.

• A. 16
• B. -16
• C. 0

Answer 1

The correct option is A 16

Let us compare $x^2+8x$ with expansion of ${(a+b)}^2$.

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

On comparing terms of RHS of above equation and $x^2+8x$, it is clear that-

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

$8x=2ab$ .... (2)

From (1) $a=x$

Substituting value of a in (2),

$8x=2\times \left(x\right)\times b$

$\Rightarrow b=4$

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

Thus, we need to add 16.

Therefore, if we add 16 to $x^2+8x$, it becomes

$x^2+8x+16=(x+4{)}^2$

which is a perfect square.