is (x^2-a^2) the same as (x-a)^2. If so would (x^2-a^2)/x-a = x-a?
x^2 - a^2 = x^2 - a^2
(x-a)^2 = x^2 - 2 a x + a^2
quite a different animal
(x^2-a^2)/(x-a)
= (x-a)(x+a) /(x-a)
= (x+a)
what you are missing is a rule to remember
a^2-b^2 = (a+b)(a-b)
No, (x^2-a^2) is not the same as (x-a)^2.
To understand why, let's look at the difference between both expressions.
First, (x^2-a^2) represents the difference of squares and can be factored as (x+a)(x-a). This is known as the difference of squares formula.
On the other hand, (x-a)^2 represents the square of the binomial (x-a), which means it is (x-a) multiplied by itself. Algebraically, it expands to (x-a)(x-a).
Therefore, (x^2-a^2) and (x-a)^2 are not equivalent.
Now, let's consider the expression (x^2-a^2)/(x-a) and see if it simplifies to (x-a).
To simplify this expression, we can factor the numerator and try to cancel out common factors. Using the difference of squares formula, we can express (x^2-a^2) as (x+a)(x-a).
Thus, the expression becomes [(x+a)(x-a)]/(x-a).
Now, we can cancel out the common factor (x-a) in the numerator and denominator, leaving us with (x+a).
Therefore, (x^2-a^2)/(x-a) simplifies to (x+a), not (x-a).