Question

Complete the expressions that would make them a perfect square trinomial.

a.
x² – 8x+
b. x2 + 20x +
C.
x² – 16x +
d. x2 + 9x +

Answer 1

a) 16

b) 100

c) 64

d)
`(81)/(4)`[/tex]

Explanation:

Perfect square trinomial:

A perfect square trinomial has the following format:

`(x \pm a)^2 = x^2 \pm 2ax + a^2`

a.

x² – 8x

`x^2 - 8x = x^2 - 2ax`

So 2a = 8, a = 4. Then

`a^2 = 4^2 = 16`

The perfect square trinomial is
`x^2 - 8x + 16`

b. x2 + 20x +

2a = 20, so a = 10

`a^2 = 10^2 = 100`

The perfect square trinomial is
`x^2 + 20x + 100`

C.

x² – 16x +

2a = -16, so a = -8.

`a^2 = (-8)^2 = 64`

The perfect square trinomial is
`x^2 - 16x + 64`

d. x2 + 9x +

`2a = 9`, so
`a = (9)/(2)`

`a^2 = ((9)/(2))^2 = (81)/(4)`

The perfect square trinomial is
`x^2 + 9x + (81)/(4)`[/tex]