## Calculus 8th Edition

$(a-b) \times (a+b)= 2(a \times b)$
$(a-b) \times (a+b)=a \times (a+b)-b \times (a+b)$ $(a-b) \times (a+b)=a \times (a+b)-b \times (a+b)= a \times a+ a \times b - b \times a- b \times b$ 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, $(a-b) \times (a+b)= 2(a \times b)$