X^2 = X*X
( A + B ) * ( A - B ) = A^2- B^2
56 * 54 = ( 55 +1 ) * ( 55 - 1 ) =
(55 +1 ) * ( 55 -1 ) = 55^2 -1^2
(A+B)*(A+B ) = A^2 + 2*A + B^2
(55)^2 = (50+5)^2
(50+5)^2 = 50^2+2*50*5+5^2
(50+5)^2 = 2500 + 500 + 25 = 3025
I am too lazy to show the proof but another shortcut is
(10X+5)^2 =(x+1)*(x)*10+25
55^2 = (6*5)*10+25 = 3025
so 56*54 = 3025 -1 = 3024
Very easy to do in your head extra steps are just to show for new learners
And with that equation they could have skipped all of the entire geometry class and just converted things about shapes into the coordinate of the parts of the shape and then used trigonometry
Geometry is a waste of time and religious mumbo jumbo about proofs that do not prove anything
Geometry should be removed from the curriculum
You just need Trigonometry, Algebra and Vector Calcululs
