What number must be added in the expression, x²-8x, to make a perfect square trinomial?

Solution:

x² - 8x [Given]

The standard form of a perfect square trinomial is

(x - a)² = x² - 2ax + a²

In the given equation add c as the value which must be added

x² - 8x + c

By equating it with the standard form

-8x = - 2ax ----->(1)

c = a²----->(2)

Solving these equations for a and c respectively, we get

-8x = - 2ax

a = -8/-2

a = 4

c = (4)² = 16

Here

(x - 4)² = x² - 8x + 16

Therefore, the value which must be added is 16.

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What number must be added in the expression, x²-8x, to make a perfect square trinomial?

Summary:

The value which must be added to the expression x² - 8x to make it a perfect square trinomial is 16.