Expanding (a+b+c)(a−b−c)
This expression represents the product of two binomials, one with a positive sign before b and c and the other with a negative sign before them. To expand it, we can use the distributive property of multiplication.
Let's break it down:

Distribute the first term (a) of the first binomial:
 a * (a  b  c) = a²  ab  ac

Distribute the second term (b) of the first binomial:
 b * (a  b  c) = ab  b²  bc

Distribute the third term (c) of the first binomial:
 c * (a  b  c) = ac  bc  c²

Combine all the terms:
 (a²  ab  ac) + (ab  b²  bc) + (ac  bc  c²)

Simplify by combining like terms:
 a²  b²  c²  2bc
Therefore, the expanded form of (a + b + c)(a  b  c) is a²  b²  c²  2bc.
Note:
 This result is similar to the difference of squares pattern, where (x + y)(x  y) = x²  y².
 The expansion highlights a specific pattern of terms when multiplying binomials with a combination of positive and negative signs.