Difference Squares II (proof without words)

This is a short animation showing one way to think of the difference of squares formula (at least when the two numbers involved are positive).

Here are three related videos:

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[xvv]

Another method, though maybe not as clever: Draw a horizontal line, along the top of the smaller square, all the way to the right side of the larger square. This divides the area into two rectangles. First, an upper rectangle, with height y-z, and width y. Second, a lower rectangle, with height z, and width y-z. Note that the height of the upper rectangle is the same as the width of the lower rectangle (i.e., both are y-z). So we can rotate the lower rectangle by 90 degrees, and append it to the right of the upper rectangle. This gives us one large rectangle of height y-z, and width y+z. Hence y^2 - z^2 = (y-z)(y+z).

[felixlafuente]

Outstanding work! This is so clear now!

[jashouse]

OMG I NEEDED THIS 2 YEARS AGO IN MY CLASS !!!!

[yplayergames]

This is exactly what I needed months ago

[aetheriox]

you could just use foil on the expanded form and see that y*y -yz + yz -z*z = y^2-z^2

[Nartymer]

why would you need to complicate it by making 2 trapezes? You can just separately take 2 rectangles that make up that shape and their area will result that.

Much more simple, intuitive and visual

[eduardopestanamarino]

Just a personal suggestion, kinder music please?

[vaagaiacademyofmathematics]

Fire 🔥 fantastic way of explaining through geometry

[Manojkumar-wejv]

op bro u are awesome plz make more videos on some most interesting maths formulas and topics

[allegrobas]

Great Visuals, BUT THE MUSIC SUCKS BIG TIME

[joefuentes]

Um you can also just foil (a+b)(a-b)= a^2 -ab +ab - b^2 and then cancel the ab... If that doesn't make sense then maybe you shouldn't Math.

[nsxkkxlnmiyo]

great, i ought to think that z then becomes a part of the difference alhotugh geometrically...where did that litle square go??

[hrishikeshaggrawal]

can you show a proof for (x+a)(x-a) peaks at a=0?

[azizurrahman]

Plz Don't add music it is annoying