when √(x²-a²)
When evaluating the expression √(x²-a²), you are finding the square root of the difference between x² and a², where a is a constant
When evaluating the expression √(x²-a²), you are finding the square root of the difference between x² and a², where a is a constant.
To simplify this expression, you can use the difference of squares identity. The difference of squares states that a² – b² can be factored as (a + b)(a – b). Comparing this to our expression √(x²-a²), we can rewrite it as √((x+a)(x-a)).
Now, you have the square root of a product inside the parentheses. To simplify further, you can split the square root into the product of square roots: √(x+a) √(x-a).
Therefore, the simplified expression for √(x²-a²) is √(x+a) √(x-a).
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