To create a perfect square trinomial from the expression x² + 8x, we need to find the value that completes the square. A perfect square trinomial can be written in the form (x + a)², where a is a constant.
To find the value, we take the coefficient of x, which is 8, divide it by 2, and then square the result:
- Step 1: Divide the coefficient of x (which is 8) by 2:
8 ÷ 2 = 4 - Step 2: Square the result:
4² = 16
Thus, the value needed to create a perfect square trinomial is 16. This means we can rewrite the expression x² + 8x as follows:
x² + 8x + 16 = (x + 4)².
This shows that by adding 16, we convert the original expression into a perfect square trinomial.