x^2+2x perfect square trinomial

Question

Determine the constant that should be added to the binomial so that it becomes the perfect square trinomial

Answer 1

x^2+2x

Recall the formula (a+b)^2 = a^2+2ab+b^2

Compare the binomial with expanded form of formula.

Here a = x, 2ab = 2x

therefore b = 1 ⇒b^2 = 1

Add 1 to given binomial.

x^2+2x+1

(x+1)^2

1 should be added to the binomial it becomes perfect squre.

 

Answer 2

x^2+2x

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 2. so, (half the x coefficient)² = (2/2)²= 1

Add 1 to the expression

x^2 + 2x + 1

Simplify the expression

(x + 1)^2