is the polynomial::
y^2-25x+25 a difference of squares, if so factor it.
Thank you so much!!
a^2-b^2 = (a-b)(a+b)
y^2 - 25(x-1)
unfortunately (x-1) is not a square of anything but (x-1)^.5 :)
I suppose you could say
[ y - 5 sqrt(x-1) ] [y + 5 sqrt(x-1) ]
but that is really stretching it
To determine if the polynomial is a difference of squares, we need to check if it can be written in the form:
(a^2 - b^2)
In this case, the polynomial is y^2 - 25x + 25.
To factor it as a difference of squares, we need to express it as (a^2 - b^2).
In order to do that, we need to see if we can rewrite our polynomial as the difference of two perfect squares.
Let's look at the first term: y^2. It is already a perfect square because it can be written as (y)^2.
Now, let's look at the last term: 25. It is also a perfect square because it can be written as (5)^2.
So, we have identified our a and b values as y and 5.
Therefore, the polynomial y^2 - 25x + 25 can be written as the difference of squares:
(y - 5)(y + 5)
Hence, the factored form of the polynomial is (y - 5)(y + 5).