(x+a)(a-x)

To simplify the expression \((x + a)(a - x)\), you can use the distributive property (also known as the FOIL method for binomials).

Here’s how it works:

\[ (x + a)(a - x) = x \cdot a + x \cdot (-x) + a \cdot a + a \cdot (-x) \]

Distributing each term:

1. \(x \cdot a = ax\)
2. \(x \cdot (-x) = -x^2\)
3. \(a \cdot a = a^2\)
4. \(a \cdot (-x) = -ax\)

Now combine all these results:

\[ ax - x^2 + a^2 - ax \]

Notice that \(ax\) and \(-ax\) cancel each other out:

\[ -x^2 + a^2 \]

Thus, the simplified form of the expression \((x + a)(a - x)\) is:

\[ a^2 - x^2 \]

This expression can also be recognized as the difference of squares, expressed as:

\[ a^2 - x^2 = (a - x)(a + x) \]

So, the result can be stated as:

\[ (x + a)(a - x) = a^2 - x^2 \]