Answer
$(a-b) \times (a+b)= 2(a \times b)$
Work Step by Step
$(a-b) \times (a+b)=a \times (a+b)-b \times (a+b)$
$(a-b) \times (a+b)=a \times (a+b)-b \times (a+b)= a \times a+ a \times b - b \times a- b \times b$
As we know, the cross product of a vector with itself is $0$.
$(a-b) \times (a+b)=a \times (a+b)-b \times (a+b)= a \times a+ a \times b - b \times a- b \times b= 0+ a \times b - b \times a- 0$
Note: $ -b \times a =a \times b$
$=a \times b + a \times b$
$= 2(a \times b)$
Hence, $(a-b) \times (a+b)= 2(a \times b)$
