Question

Is there anyone who can help me with this problem please!!! \[4x^4+8x^2+9\] force a perfect square trinomial in order to factor as a difference of squares:

Answer 1

\[4x^4+8x^2+9\]

Answer 2

This shows how to do it
http://www.khanacademy.org/math/algebra/quadratics/completing_the_square/v/solving-quadratic-equations-by-square-roots

Answer 3

ty,,,,, i have been workng on it for over an hour

Answer 4

you could do this. factor 4 out of the first 2 terms:
4 (x^2 + 2x ) + 9

take the coefficient on the x term (the 2) divide it by 2 and square it.
2/2 is 1. 1 squared is 1. add +1 and -1 inside the parens

4 (x^2 + 2x +1 - 1) + 9
(+1-1 is 0 , so we have not changed the value)
now write this as
4 (x^2 + 2x +1) -4*1 +9
(we distributed the 4 to move the -1 outside the parens.
simplify to get
4(x^2 + 2x +1) +5

the stuff inside the parens is a perfect square (x+1)^2 so this is
4 (x+1)^2 +5

Answer 5

normally you would do this when solving the equation
4 x^2 + 8x + 9 =0

in that case people often "move the 9" to the other side: add -9 to both sides
4 x^2 + 8x = -9
again factor out the 4
4(x^2 + 2x) = -9
divide both sides by 4
x^2 +2x = -9/4

now do the "complete the square" : divide the coefficient on the x term by 2
that means 2/2 =1
square the result: 1*1= 1
that means add +1 to both sides of the equation
x^2 +2x +1 = -9/4 +1
(notice that add +1 to both sides is instead of adding +1 -1 to one side)
now the left side is
(x+1)^2 = -5/4

normally we would take the square root of both sides to solve for x. in this case the right side is negative, so we will get an imaginary number. depending on what class you are in, that is advanced stuff.

Answer 6

this is algebrra 2,, and way over my head,, tyytyt vvv much!

Answer 7

in this case you have x^4 and x^2, so the answer would be
\[ 4 (x^2+1)^2 +5 \]

however, this is not a difference of squares (if that 5 where -4 or -9 it would be)
Do you have the correct question ?

Answer 8

yes the question is correct

Answer 9

if we assume we can use imaginary numbers we could proceed this way
\[ 4 (x^2+1)^2 - (-5) = (2(x^2+1)+ \sqrt{5}i)(2(x^2+1)- \sqrt{5}i)\]
but it does not look pretty.