Visual math proof x² - y² = (x + y)(x - y)

Visual explanation of the difference of squares formula from math class. #shorts #math #maths #mathematics

The Difference - The Wallflowers

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Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!

If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.

Book ratings are from January 2023.

My Books (worldwide links)

My Books (US links)
Mind Your Decisions: Five Book Compilation
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews

Mind Your Puzzles: Collection Of Volumes 1 To 3
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

My Blog

Twitter

Instagram

Merch

Patreon

Press

[VitaliyCD]

This is the most satisfying thing I have seen all week.. And I do math every workday. 😹

[hexagonaldimencion]

Could you explain: x^3+y^3=yx(x+y)+(x-y)^2(x+y) ?

[the_eternal_doomslayer]

This blew my mind on multiple levels at the same time
Now I feel like a interdimensional god

[serkratos]

now explain difference of cubes geometrically.

[MiguelSucksAtUrbanism]

I love watching notable products visual proofs

[wewe-fxun]

That's how it was taught to us.
--An Indian

[icosahedron]

Please show it with equilateral triangles too

[ZerCraftGaming]

Out of everything of yours I watched - this is the most impactful (for me)

[wabbatal]

I just wish schools would show proofs instead of just telling us to memorize this stuff

[jixinyi]

As a formal Algebra student I think it easier to just know it the traditional way but I guess this works for a lot of people

[wesleysuen]

What about an animation for the difference of cubes formula as well?

[asdf_]

can Be Done through Algebra ie Factor Remainder.

[nvapisces]

Formula for difference of n powers is just x-y multiplied with another expression that builds up the powers for x multiplied with the reduce in power for y aka (x-y)(x^n*y^0 + x^(n-1)*y^1 +...+ x^0*y^n). Coefficients are all 1 for every term.

[jplbkqx]

I wish you were my 8th grade math teacher.

[GCSEALevelMaths]

That’s so cool and satisfying lol. Loved it.

[Creamcheese]

a²-b² can be written as
a²+b²+2ab -2b²-2ab
= (a+b)² - 2b²-2ab
=(a+b)²-2b(a+b) {taking -2b common}
=(a+b){a+b-2b} [taking (a+b) common]
= (a+b)(a-b) proved

[stevensullivan]

The math is obviously correct and this is a lovely visualization, but the best part of the video is definitely the song choice. Well played!

[aguyontheinternet]

Really cool, but this is also really easy to prove through just taking x^2-y^2 and working it into the equation.

[DataStorm]

Psst: suprise *long badword starting with M*: y > x negative space!

[sparshsharma]

Apart from topic, Completing the square is pretty easy what about visualisation of completing the cube?