will medal for help Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

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will medal for help Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

Mathematics
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let sin x= a and cos = b to make it look s easier :P \[\huge\rm (a-b)^2+(a+b)^2\] familiar wit the foil method ?
ive heard of it before but I cant remember how it goes
alright (a-b)^2 is same as (a-b)(a-b)|dw:1439569755635:dw| first multiply first term with the 2nd parentheses and then multiply 2nd term of 1st parentheses by 2nd one

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alright how would i apply that to this problem?
so sin = a b= b (a-b)(a-b) apply the foil method \[\huge\rm \color{reD}{a}(a-b) \color{reD}{- b}(a-b)\] distribute
I'm sorry im still confused? are we to plug in numbers or just the letters?
well we don't have to i just change cos and sin with a b to make it a little bit easier
oh okay I understand whats next?
(a-b)(a-b) apply the foil method \[\huge\rm \color{reD}{a}(a-b) \color{reD}{- b}(a-b)\] distribute (a-b) by a and then (a-b) by -b
|dw:1439570120307:dw| multiply both terms by a a times a - a times b = ?
a^2 - b times a?
yes right -b(a-b) =?
ot would it just be (a-b)^2
no
\(\color{blue}{\text{Originally Posted by}}\) @macim a^2 - b times a? \(\color{blue}{\text{End of Quote}}\) this is right for first part
oh alright! and then it would be a times b -b^2?
well it is -b(a-b) signs!!!
-b times a = ?
wouldn't it just equal -b times a because you cant multiply those variables?
yes negative ab -ab so -b times -b = ??
-2b?
no b times b is b^2 is right but there is sign mistake negative times negative = ?
oh right sorry it would just be 2b
or b^2
yes right
the b^2 is right or 2b?
b^2 when you multiply same bases you should add their exponents
now write it together|dw:1439570550698:dw| \[\huge\rm a^2-ab-ab+b^2\] combine like terms
would you just end up with a^2+b^2
-ab-ab=??
i thought they would just cancel each other out. but if they don't wouldn't it be ab^2
no both terms are same and same sign so you can't** cancel them \[\rm a-a= 0~~~-a-a=-2a\] when you add or subtract like terms just simply add or subtract their coefficients and when you multiply same bases then you should add their exponents \[\rm x^1 \times x^1= x^{1+1}\]
-ab-ab is same as \[\huge\rm \color{red}{-1}ab\color{red}{-1}ab=(-1-1)ab\]
alright i understand that
so it's equal to -2ab ? right or no?
yes?
i'm asking yes or no ?
yes
-ab-ab is same as \[\huge\rm \color{red}{-1}ab\color{red}{-1}ab=(-1-1)ab=-2ab\]
so \[\huge\rm (a-b)^2=a^2-2ab+b^2\] now 2nd part of the question (a+b)^2 which is same as (a+b)(a+b) foil it!
foil (a-b)^2=a^2-2ab+b^2?
yea that's for (a-b)^2 now foil (a+b)^2
I'm sorry I really don't understand?
like i said (a+b)^2 is same as (a+b)(a+b) now just multiply like we did for (a-b)^2
or in other words square of first number and square of 2nd number and multiply both terms by 2 here is an example |dw:1439571636107:dw| just like this
would it just be a^2+b^2
no llook at the drawing ^^^^
a^2+2b^2+2?
|dw:1439571972434:dw| there should be 3 terms
so would I have to make up another because we only have 2
well you don't make up you need to know how to foil method works let's try box method to foil binomial |dw:1439572122692:dw| write one parentheses at the top of the box and one left side now start multiplying terms
so a^2+b^2+ab+2b
how did you get 2b ?
because of b times b
but that would b^2 wouldn't it
yes right so how did you get 2b ?
|dw:1439572443606:dw| now multiply a+b by b and write it down in the box
|dw:1439572494627:dw|