Simplify (x+y+z)(x-y-z)

Problem

(x+y+z)*(x−y−z)

Solution

1. Group the terms to identify a difference of squares pattern by rewriting the expressions.

(x+(y+z))*(x−(y+z))

2. Apply the difference of squares formula, which states that (a+b)*(a−b)=a^2−b^2 where a=x and b=(y+z)

x^2−(y+z)^2

3. Expand the squared binomial (y+z)^2 using the identity (a+b)^2=a^2+2*a*b+b^2

x^2−(y^2+2*y*z+z^2)

4. Distribute the negative sign to all terms inside the parentheses to reach the final simplified form.

x^2−y^2−2*y*z−z^2

Final Answer

(x+y+z)*(x−y−z)=x^2−y^2−2*y*z−z^2

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