When a polynomial is multiplied by itself, then it is a perfect square. Example – polynomial ax² + bx + c is a perfect square if b² = 4ac.

Perfect Square Formula is given as,

\[\large \left(a+b\right)^{2}=a^{2}+2ab+b^{2}\]

Solved Example

Question: Is x² + 10x + 25 a perfect square or not ?

Solution:

x² + 10x + 25
= x² + 10x + (5

 5)
= x² + 10x + 5²
= x² + 2(5  x) + 5²
= (x + 5)²

So, x² + 10x + 25 is a perfect square.