Question

should be added to ${4x}^2-4x$ to make it a perfect square.

• A. 1
• B. -1
• C. 0

Answer 1

The correct option is A 1

Let us compare ${4x}^2-4x$ with expansion of ${(a+b)}^2$.

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

On comparing terms of RHS of above equation and $4x^2-4x$, it is clear that-

$a^2=4x^2$ .... (1)

$-4x=2ab$ .... (2)

From (1) $a=2x$

Substituting value of a in (2),

$-4x=2\times \left(2x\right)\times b$

$\Rightarrow b=-1$

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

Thus, we need to add 1.

Therefore, if we add 1 to ${4x}^2-4x$, it becomes

${4x}^2-4x+1=(2x-1{)}^2$

which is a perfect square.