Complete the square for the following binomial Then factor t

Complete the square for the following binomial Then factor the resulting perfect square trinomial. X^2+ 1/3^x Complete the square. What is the resulting perfect square trinomial? (Do not factor.) Factor the resulting perfect square trinomial.

Solution

x^2 +x/3

x^2 +x/3 + (1/6)^2 - (1/6)^2

(x +1/6)^2 - (1/36) ----> Perfect square of form (a+b)^2

Use the formula : a^2 - b^2 = (a+b)( a- b)

So, (x +1/6)^2 - (1/36) = (x+1/6 -1/6)(x+1/6 +1/6)

= x(x +1/3) ----> ( Factorised form)