Which value is needed to create a perfect square trinomial from the expression x² + 8x + _____?

Solution:

Given, the expression is x² + 8x + C --- (1)

A perfect square is an expression in the form (x+a)² which can be written in the trinomial form as:

(x + a)² = (x + a)(x + a) = x² + ax + ax + a²

(x+a)² = x² + 2ax + a² --- (2)

Comparing (1) and (2)

2a = 8

a = 4

Also, a² = C

C = (4)² = 16

Therefore, the expression is x² + 8x + 16.

Which value is needed to create a perfect square trinomial from the expression x² + 8x + _____?

Summary:

The value which is needed to create a perfect square trinomial form of the expression is x² + 8x + ___ is 16.