If x^2 + mx + m is a perfect-square trinomial, which equation must be true?

a. x^2 + mx + m = (x - 1) ^2

b. x^2 + mx + m = (x + 1) ^2

c. x^2 + mx + m = (x + 2) ^2

d. x^2 + mx + m = (x + 4) ^2

If x^2 + mx + m is a perfect-square trinomial, it means the squared value will have a positive number inside because the value of 'm' is positive and it should be equal to the middle term too, as the middle term and the last terms are same in the trinomial.

So from the given equations:

we can conclude that:

b. x^2 + mx + m = (x + 1) ^2

because:

(x + 1) ^2 = x^2 + 2x + 1