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asnaseerBest ResponseYou've already chosen the best response.1
which aspect is troubling you here?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
ok, first step is to remove the braces. do you know how to remove the braces? especially the braces with the minus sign outside of it.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
ok  the rule here is that any expression within braces remains "asis" when the braces are removed unless the braces have a minus sign outside of them. In that case all the signs inside the braces change  i.e. all ""'s change to "+" and all "+"'s change to ""
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
e.g.: (1+45) + (63)  (2+41) = 1+45 + 63 24+1
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
does that make sense so far?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
good, so now try to use these rules to remove the braces in your expression
 one year ago

vortishBest ResponseYou've already chosen the best response.0
\[2x ^{4}y ^{3}+4x ^{3}y ^{4}5x ^{4}y ^{3}+6x ^{3}y ^{4}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
perfect! now you just need to combine "like" terms
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
do you know what "like" terms are?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
no  that is not quite right
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
the way to think about this might be to imagine each unique combination of products of powers of x and y as a separate entity. e.g. in \(3x^3y^2+2x^2y^3x^3y^2\) we have two unique combinations, namely: \(x^3y^2\) and \(x^2y^3\)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
think of each of these combinations as a new "variable". so, in the example I gave, let \(A=x^3y^2\) and \(B=x^2y^3\). we can then write my expression as: \(3x^3y^2+2x^2y^3x^3y^2=3A+2BA=2A+2B\) make sense?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
is it one specific part here that is unclear or the whole thing?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
ok  so you understand how I picked out the two unique combinations of powers of x and y in my initial expression  correct?
 one year ago

vortishBest ResponseYou've already chosen the best response.0
that is where i am having the issue
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
ok  lets take a look in more detail. we have the expression: \(3x^3y^2+2x^2y^3x^3y^2\) do you agree that this contains terms that involve multiples of \(x^3y^2\) and \(x^2y^3\) only? i.e. there are no other "combinations" of powers of x and y within my expression.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
now, the next step I took was to replace all occurrences of \(x^3y^2\) by a new variable that I called \(A\). this leads to: \(3x^3y^2+2x^2y^3x^3y^2=3A+2x^2y^3A\) make sense so far?
 one year ago

vortishBest ResponseYou've already chosen the best response.0
ok i think that make sense
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
good  the next step was to tackel the remaining unique combination which was \(x^2y^3\)  I replaced all occurrences of this with another new variable that I called \(B\). this leads to: \(3x^3y^2+2x^2y^3x^3y^2=3A+2x^2y^3A=3A+2BA\) ok so far?
 one year ago

vortishBest ResponseYou've already chosen the best response.0
so i would come up with 3x^4y^3 +7x^3y^4
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
good  now we just simplify our new expression by combining all terms involving \(A\) and separately all terms involving \(B\). this leads to: \(3x^3y^2+2x^2y^3x^3y^2=3A+2x^2y^3A=3A+2BA\) = \(3AA+2B\) = \(2A+2B\)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
your expression after removing the braces was:\[2x ^{4}y ^{3}+4x ^{3}y ^{4}5x ^{4}y ^{3}+6x ^{3}y ^{4}\] so if you first replace \(x^4y^3\) by \(A\) and \(x^3y^4\) by \(B\) then you would get:\[2x ^{4}y ^{3}+4x ^{3}y ^{4}5x ^{4}y ^{3}+6x ^{3}y ^{4}=2A+4B5A+6B\] what do you think that simplifies to in terms of A and B?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
correct  now just replace A and B by what they represent
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
the "trick" is to recognise these "unique" combinations of terms  that is what is meant by "like" terms in an expression.
 one year ago

vortishBest ResponseYou've already chosen the best response.0
got it right thanks asnaseer
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
it is similar to saying: 2*apples + 3*pears  5*apples = 3*apples + 3*pears i.e. you cannot combine "apples" and "pears"
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
ok  glad you got it now
 one year ago
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