Factor completely
(x+y)^2-25
The given expression can be factored using the difference of squares formula, which states that for any two numbers a and b, the expression (a^2 - b^2) can be factored as (a+b)(a-b).
In this case, we have the expression (x+y)^2 - 25.
Using the difference of squares formula, we can rewrite this as ((x+y) + 5)((x+y) - 5).
So, the expression (x+y)^2 - 25 factors completely as ((x+y) + 5)((x+y) - 5).
To factor the expression (x+y)^2 - 25, you can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).
In this case, let's treat (x+y)^2 as "a^2" and 25 as "b^2". So, we have:
(a^2 - b^2) = ((x+y)^2 - 5^2)
Applying the difference of squares formula, we get:
((x+y)^2 - 5^2) = ((x+y+5)(x+y-5))
Therefore, the expression (x+y)^2 - 25 can be factored completely as (x+y+5)(x+y-5).
To factor the expression (x+y)^2 - 25 completely, we can recognize it as the difference of squares. The expression (x+y)^2 can be expanded using the formula for the square of a binomial: (x+y)^2 = x^2 + 2xy + y^2.
Substituting this into the given expression, we have x^2 + 2xy + y^2 - 25.
Now, we notice that the terms x^2 + 2xy + y^2 can be factored as (x+y)(x+y) or (x+y)^2. This leaves us with (x+y)^2 - 25.
Applying the formula for difference of squares, we have (x+y)^2 - 25 = [(x+y) + 5][(x+y) - 5].
Therefore, the expression (x+y)^2 - 25 factors completely as (x+y+5)(x+y-5).