Difference between revisions of "User:Sapphiredove41"
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| − | + | Proof that <math>(x + y)^2</math> and <math>x^2 + y^2</math> are the same when <math>x</math> or <math>y</math> is <math>0</math>: | |
| + | <math>(x+y)^2</math> factored out is <math>x^2+2xy+y^2</math>, so if we want to make the statement <math>(x+y)^2=x^2+y^2</math> true, <math>2xy</math> must be equal to <math>0</math>. | ||
| + | This means that either <math>x</math> or <math>y</math> has to be <math>0</math> for this to work. We can see this if we substitute <math>0</math> in for <math>y</math> | ||
| + | <cmath>(x+0)^2=x^2</cmath> | ||
| + | <cmath>x^2+0^2=x^2+0=x^2</cmath> | ||
Latest revision as of 15:52, 22 February 2025
Proof that 
and 
are the same when 
or 
is 
:
factored out is 
, so if we want to make the statement 
true, 
must be equal to .
This means that either or has to be for this to work. We can see this if we substitute in for
![\[(x+0)^2=x^2\]](http://latex.artofproblemsolving.com/f/3/b/f3be1792f17807262dc05d7bc86d8864ef3a026f.png)
![\[x^2+0^2=x^2+0=x^2\]](http://latex.artofproblemsolving.com/a/b/b/abb0dde56e810af6e1e2be78e01bf1d3ec6b35e3.png)
