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