(4+х)(x-4)

To expand the expression \((4+x)(x-4)\), you use the distributive property (also known as the FOIL method for binomials).

Here's how it goes:

\[ (4+x)(x-4) = 4 \cdot x + 4 \cdot (-4) + x \cdot x + x \cdot (-4) \]

Now, calculate each term:

1. \(4 \cdot x = 4x\)
2. \(4 \cdot (-4) = -16\)
3. \(x \cdot x = x^2\)
4. \(x \cdot (-4) = -4x\)

Now, combine the like terms:

\[ 4x - 4x + x^2 - 16 \]

The \(4x\) and \(-4x\) cancel each other out, leaving you with:

\[ x^2 - 16 \]

So, the expanded form of the expression \((4+x)(x-4)\) is:

\[ x^2 - 16 \]

This can also be recognized as a difference of squares, which can be factored further into \((x-4)(x+4)\) if needed.