Hi can anyone help me with this question? It's about arranging expressions.

mather

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Aug 23, 2013
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So they gave me this. a^2+2ab+b^2 -x^2-6x-9.

They said " factor the expression. Begin by arranging it as follows.

(1) arrange it with a as variable.
(2) arrange it with b as variable
(3) as a difference of two squares


I understand that they want be to arrange it three different ways and solve and come to the same conclusion because the next page says use any of the three ways. However, when i look at it, I can only see it as a difference of squares. For a bit of context, they were making me do factoring of squared expressions with three terms in the brackets. kinda like (a+b+c)2.
 
So they gave me this. a^2+2ab+b^2 -x^2-6x-9.

They said " factor the expression. Begin by arranging it as follows.

(1) arrange it with a as variable.
(2) arrange it with b as variable
(3) as a difference of two squares


I understand that they want be to arrange it three different ways and solve and come to the same conclusion because the next page says use any of the three ways. However, when i look at it, I can only see it as a difference of squares. For a bit of context, they were making me do factoring of squared expressions with three terms in the brackets. kinda like (a+b+c)2.
It would help a lot if we knew the full problem statement, including what is on that second page. I think what they mean by # 1 is

\(\displaystyle a^2 + 2ab + b^2 - x^2 - 6x - 9 = a(a + 2b) + b^2 - (x + 3)^2 = a(a + 2b) + (b - x - 3)(b + x + 3).\)
 
So they gave me this. a^2+2ab+b^2 -x^2-6x-9.

They said " factor the expression. Begin by arranging it as follows.

(1) arrange it with a as variable.
(2) arrange it with b as variable
(3) as a difference of two squares


I understand that they want be to arrange it three different ways and solve and come to the same conclusion because the next page says use any of the three ways. However, when i look at it, I can only see it as a difference of squares. For a bit of context, they were making me do factoring of squared expressions with three terms in the brackets. kinda like (a+b+c)2.

a^2 + 2ab + b^2 - x^2 - 6x - 9

= (a+b)^2 - (x+3)^2

= (a+b+x+3)(a+b-x-3)
 
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