$$(u+v)\cdot(u- v)= -8.$$
Work Step by Step
We have $$(u+v)\cdot(u- v)=u\cdot u-u\cdot v+v\cdot u-v\cdot v=\| u\|^2-\| v\|^2\\ = 1^2-3^2=1-9=-8.$$
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