Proof for trick to multiply fast

73 Views Asked by At

lets say we want to multiply 78*94

we multiply the first number by the third then we multiply the second by the fourth we get 6332 next we multiply 2nd and 3d + 1st and 4th we get 100 we add this to our previus number shifted 1 to the left we get :

7332

$$7*9 = 63$$ $$8*4 = 32$$ $$n = 6332 +1000$$ is there any proof for this and how can this be done with bigger numbers?