(х+1)(х-1)+7

The expression you provided is a multiplication of two binomials followed by an addition of a constant. To simplify this expression, you can use the distributive property, also known as FOIL (First, Outer, Inner, Last) method for binomials, or recognize it as a difference of squares pattern.

Here is the expression again for clarity: (х + 1)(х - 1) + 7

We can recognize that (х + 1)(х - 1) is in the form of (a + b)(a - b), which is a difference of squares. The difference of squares can be simplified to \(a^2 - b^2\).

So using the variables from your expression:

\( a = x \) \( b = 1 \)

Using the difference of squares formula: \(a^2 - b^2 = (x)^2 - (1)^2 = x^2 - 1\)

When we add the constant 7, we get: \(x^2 - 1 + 7\)

Simplify by combining like terms (the constants): \(x^2 + 6\)

So the simplified form of the expression is: \(x^2 + 6\)

That would be the final simplified expression for the given input.