Answer:
x^2 - 7
Explanation:
To simplify the expression (x + √7)(x - √7), we can use the distributive property of multiplication:
(x + √7)(x - √7) = x(x) + x(-√7) + √7(x) + √7(-√7)
Now, let's simplify each term:
x(x) = x^2
x(-√7) = -x√7
√7(x) = √7x
√7(-√7) = -7
Combining all the terms:
x^2 - x√7 + √7x - 7
We can rearrange the terms:
x^2 + (√7x - x√7) - 7
Notice that (√7x - x√7) simplifies to 0 since the two terms cancel each other out. Therefore, we have:
x^2 - 7
Thus, the simplified form of (x + √7)(x - √7) is x^2 - 7.
Hope this helps!