Question

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}+50 x$$

Short answer

The term that should be added is 625.

Step-by-step solution

Identifying the values of 'a' and 'b'

In the given expression, 'a' corresponds to the coefficient of \(x^2\), which is 1. 'b' corresponds to half of the coefficient of 'x', which is \(50/2 = 25\).

Adding square of 'b' to the expression

To make it a perfect square trinomial, we add the square of 'b' to the expression, which gives us \(x^{2} + 50x + 25^2\).

Completion

After adding the square of 'b' to the original expression, we now have a perfect square trinomial. Therefore, the term that should be added to the original expression is \(b^2 = 25^2 = 625\).