To simplify the expression (x – y – z)² – (x + y + z)², we can use the difference of squares factorization \(a^2 - b^2 = (a+b)(a-b)\), where \(a = (x - y - z)\) and \(b = (x + y + z)\).
Applying this factorization, we get:
\((x - y - z)^2 - (x + y + z)^2 = [(x - y - z) + (x + y + z)][(x - y - z) - (x + y + z)]\)
Simplifying the terms inside the brackets:
\( = [x - y - z + x + y + z][x - y - z - x - y - z]\)
\( = [2x][-2y - 2z]\)
\( = 2x[-2(y + z)]\)
\( = -4x(y + z)\)
Therefore, the simplified expression is \( -4x(y + z) \).
Thus, the correct option is 2. -4x(y + z)
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