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complete square and stuff... for sum of squares
Lmao I'm still confused...I'm sorry:/
There is no formula for the "sum of two squares." The formula for the "difference of two squares" is it equals sum of two numbers times their difference.
I kinda get it but I don't get the drawing above^^^^
isnt the sum of 2 squares: (a-bi)(a+bi) complex conjugates
This^ is all you need to know :)
Prove it to yourself using FOIL.
Or the distributive property of multiplication.
So is that the sum or the difference?
Okay nd for the sum there is no formula,right??
So then how do you factor the sum?
$$a^2-b^2$$ a is squared and b is squared and we are looking at the difference between them.
You can not factor the sum.
Oh I see:) Thank you for actually trying to understand nd explain to me how to do it unlike the others:)
Thank you for trying to learn :)
\[a^2+b^2=(a+bi)(a-bi)\] but if you are only concerned with factoring across the Real numbers, than it is considered prime
Wait I'm confused again
I need an example for each though
@Shawna.marie you don't need to worry about complex numbers like a +bi
You are working with the Real numbers.
the fundamental thrm of algebra says that the maximum number of roots (or solution to f(x)=0) of a polynomial relates to the degree of the polynomial x^2 + 9 has 2 roots, to solution to x^2+9 = 0 what it does not tells us is if those solutions are Real numbers or not.
I need an example for each I am still kinda confused
x^2 + 9 is an example of the sum of 2 squares
What about the difference nd what would the two squares for ^^^that one be?
Don't worry about the sum of two squares, you will only confuse yourself.
there are 3 parts to the expression, one of them is an operation (+) the other 2 parts are terms, in this case each term is called a "square" since they are of the form n^2
Concentrate on understanding the DIFFERENCE of two squares formula: $$a^2-b^2=(a+b)(a-b)$$
Okay so I get that one but what would an example be?
Try making your own examples by choosing numbers for a and b.
The best way to come up with complete sentences about the "difference of two squares." Is to provide your own explanation and examples :)