Evaluate the product (5+6+7)(−5+6+7)(5−6+7)(5+6−7).
Solution — click to reveal
Using the difference-of-squares factorization repeatedly, we have (5+6+7)(−5+6+7)(5−6+7)(5+6−7)=((6+7)2−(5)2)((5)2−(6−7)2)=((13+242)−5)(5−(13−242))=(242−8)(242+8)=(242)2−82=168−64=104.