how do i make a perfect square trinomial

Question

amistre64 · Answer

by squaring some unexpecting little binomial

amistre64 · Answer

(x+n)^2

(x+n) (x+n)

expand it out with distribution ...

anonymous · Answer

okay say the binomial was x^2+16x how would i work this? @amistre64

amistre64 · Answer

you cant make that a perfect square .... you would have to add something to it.

the key is in the binomial expansion tho:

$$(x+n)(x+n)=x^2+2n~x+n^2$$

anonymous · Answer

i know that but how do i work it to find what number it would be

amistre64 · Answer

notice that the term of x, it has a 2n in from of it

if we could solve for n, all we would need to do is modify the original problem by $\pm n^2$

amistre64 · Answer

x^2 + 2n x + n^2  ,  is a complete square

x^2 + 16 x  , is not a complete square

so, when 2n = 16;  we can determine a suitable value for n^2

anonymous · Answer

okay, i think im lost

amistre64 · Answer

... youll have to be more exacting about the confusion

anonymous · Answer

i don't understand any of it

amistre64 · Answer

so when you said:  i know that but how do i work it to find what number it would be.  You actually meant what?

amistre64 · Answer

(x+n)^2 defines a perfect square

(x+n)^2 = (x+n)(x+n) = x^2 + 2n x + n^2 
                                     ^^^^^^^^^^^^^^
                                       this is the format for a perfect
                                          square trinomial

amistre64 · Answer

all you have to do is compare parts now

anonymous · Answer

okay thank you

amistre64 · Answer

so tell me:

x^2 + 2n x + n^2  compares to
x^2 + 16 x

do you agree that 2n = 16?

anonymous · Answer

yes, i do sorry its taking so long its raining here

amistre64 · Answer

getting cloudy over here, and my paying job is vieing for my attention as well :)

anonymous · Answer

lol ha where you live?

amistre64 · Answer

so,  if 2n = 16,  then n=8

adding n^2 is therefore just adding 8^2 to the setup

FL

anonymous · Answer

cool lol im in LA ok but 8^2=64 right?

amistre64 · Answer

64 yes

anonymous · Answer

so that would be my final answer right?

amistre64 · Answer

if you are looking to make that into a complete (perfect) square, then yes

x^2 + 2n x + n^2  compares to
x^2 + 16 x + 64

anonymous · Answer

thank you!

amistre64 · Answer

youre welcome, and good luck

anonymous · Answer

be safe down there is FL its suppose to get bad!