Factor completely. Assume that variables in exponents represent positive integers.
x^2a-y^2
(x√a + y)(x√a - y)
Did you mean for that "a" to be there?
yes there's an a
To factor completely the expression x^(2a) - y^(2), we need to identify a difference of squares.
A difference of squares is a special case of factoring that occurs when we have the difference of two perfect squares.
In this case, we have x^(2a) - y^(2), which can be rewritten as (x^(a))^2 - (y)^2.
Using the formula for the difference of squares, we can factor it as follows:
(x^(a))^2 - (y)^2 = (x^a + y)(x^a - y)
Therefore, the expression x^(2a) - y^(2) factors completely as (x^a + y)(x^a - y).
To factor completely, we need to express the given expression in the form of a product of simpler expressions. Let's factorize the expression x^2a - y^2.
In this case, we have a difference of squares, which can be factored using the formula (a^2 - b^2) = (a + b)(a - b).
Using this formula, we can rewrite the expression:
x^2a - y^2 = (x^a)^2 - y^2
Now, we have a^2 = (x^a)^2 and b^2 = y^2.
So, applying the formula, we get:
(x^a)^2 - y^2 = (x^a + y)(x^a - y)
Therefore, the completely factored form of the expression x^2a - y^2 is (x^a + y)(x^a - y).