Question

What number should be added to $x^2+12x$ to make it a perfect square?

• A. 144
• B. 36
• C. 18
• D. 72

Answer 1

The correct option is B

36

Using the algebraic identity $(a+b{)}^2=(a^2+2ab+b^2)$
$x^2+12x$$\Rightarrow x^2+2\left(x\right)\left(6\right)$

This is of the form $a^2+2ab$. If the term $b^2$ is added, it will become a perfect square of the form $(a+b{)}^2$
So here $6^2$ i.e. 36 must be added to $x^2+12x$ to make it a perfect square of the form $(x+6{)}^2$