As someone who only learned multivariable calculus successfully via independent study of exterior differential forms as a result of off-handed comments from the differential geometry professor who taught my first-year calc course, I wholeheartedly agree.

Oh, and 12×17 = 10×17 + 2×17 = 10×17 + 2×10 + 2×7 = 170 + 20 + 14 = 204.