Perfect Square Formula

Perfect Square Formula

When a polynomial is multiplied to itself, it results in a perfect square polynomial. 

The perfect square formula is given by the following expression:

(a + b)² = a² + 2ab + b²


How to Check Whether a Given Polynomial is a Perfect Square or Not?

To check whether a given polynomial, ax2 + bx + c is a perfect square or not, we just check the relation b2 = 4ac is satisfied or not. If the relation b2 = 4ac is satisfied, then the given polynomial is a perfect square.


Solved Examples


Q 1. Check Whether the Polynomial x2 + 6x + 8 is a Perfect Square or Not.


Solution :

Comparing the given polynomial x2 + 6x + 8 with the standard polynomial ax2 + bx + c, we get the values of a = 1, b = 6 and c = 8.

Now, check the relation b2 = 4ac is satisfied or not

LHS: b2 = 62 = 36

RHS: 4ac = 4 x 1 x 8 = 32

Here, LHS ≠ RHS. The relation is not satisfied i.e., b2 ≠ 4ac.

Therefore, the given polynomial x2 + 6x + 8 is not a perfect square.


Q 1. Check Whether the Polynomial x2 + 8x + 16 is a Perfect Square or Not.


Solution :

Comparing the given polynomial x2 + 8x + 16 with the standard polynomial ax2 + bx + c, we get the values of a = 1, b = 8 and c = 16.

Now, check the relation b2 = 4ac is satisfied or not

LHS: b2 = 82 = 64

RHS: 4ac = 4 x 1 x 16 = 64

Here, LHS = RHS. The relation b2 = 4ac is satisfied.

Therefore, the given polynomial x2 + 8x + 16 is a perfect square.