How in the world do you do a perfect square, minus a perfect square trinomial in factored form?

Question

9-(a^2+2ab+b^2)
how do you work that one out?!
I am in calculus, and in algebra, this is the first time I've encountered a problem I couldnt easily do, let alone be stumped!

Answer 1

9- (a^2 +2ab+b^2)

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

[Applying (a^2) - (b^2) = (a+b) (a-b), we get,]

=(3+a+b)(3-a-b) --- Ans

Is that what you want?

Answer 2

What you have is the difference of two squares. Use the general rule: x² − y² = (x+y)(x-y).

In your case, x is "3", and y is "(a+b)".

9 − (a² + 2ab + b²)
= 9 − (a+b)²
= 3² − (a+b)²
= (3 + (a+b))(3 − (a+b))

Answer 3

This is the same as

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

a = 3
and b = (a + b)

for your problem so

the answer is (3 - (a + b))(3 + (a + b))

Answer 4

Using identity x^2 - y^2 = (x-y)(x+y)

In this case
9 - (a+b)^2 = (9-(a+b))(9+(a+b))