find whether an algebraic expression is a perfect square.can anyone help me to find out whether an algebraic equation is a perfect square or not? If not make it a perfect square.  

giorgiana1976 | Student

Let's discuss about the square of a binomial.

(a+b)^2 = a^2 + 2a*b + b^2

(a - b)^2 = a^2 - 2a*b + b^2

The square of a binomial yields 3 terms.

How come? Let's see. We'll determine the result of (a+b)^2 using FOLI method:

(a+b)(a+b) = a^2 + a*b + b*a + b^2

We'll combine like terms:

(a+b)^2 = a^2 + 2a*b + b^2

a^2 is the square of a

b^2 is the square of b

Let's recognize a perfect square:

x^2 + 50x + 100

We notice that x^2 is the square of x and 100 is the square of 10. The middle terms has to be twice the product of the terms x and 10, namely 10 x. Instead, we have 50 x.

So, the quadratic is not a perfect square.

Let's make a perfect square:

x^2 + 50x + 100 = (x^2 + 10x + 100) + 40x = (x+10)^2 + 40x