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)=a2−b2 where a=x and b=(y+z)

x2−(y+z)2

3. Expand the squared binomial (y+z)2 using the identity (a+b)2=a2+2*a*b+b2

x2−(y2+2*y*z+z2)

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

x2−y2−2*y*z−z2

Final Answer

(x+y+z)*(x−y−z)=x2−y2−2*y*z−z2

Want more problems? Check here!