To form a perfect square trinomial from the expression x² + 6x, we need to add a constant that allows us to express it as a square of a binomial.
A perfect square trinomial takes the form (a + b)² = a² + 2ab + b². In our case, a is x and 2b corresponds to the 6 in the linear term.
To find b, we calculate:
- 2b = 6
- Dividing both sides by 2 gives b = 3.
The constant we need to add to x² + 6x is the square of b:
- b² = 3² = 9
Therefore, by adding 9 to the expression, we get:
x² + 6x + 9 = (x + 3)²In conclusion, to form a perfect square trinomial from x² + 6x, you need to add 9.