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secondary 3 | A Maths
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need help with part b only,, dont rly know what they are anking for in (i) and (ii)
Date Posted: 3 years ago
Views: 227
part b the equation is (4/x^2-3x^2)^8
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3 years ago
for the expansion part we need to separate the terms in the bracket if possible?
i dont understand the finding term independent of x part tho
Yes, we need to separate the individual numbers and group all the x together.
The expansion of any binomial expression is basically the sum of many individual terms in the expansion.
For example, (1 + x)^2 = 1 + 2x + x^2 after simplification. Each of these three individual terms are referred to as individual terms.
A general term is basically a particular term (raised to a power of x) in the full expansion. Sometimes, we wish to know the coefficient of some power of x inside the expansion, but we do not wish to expand out binomially (or worse, manually) because the power is extremely large and the term to find happens to be in the middle.
In such a case, finding out the general term would be more appropriate. Different terms in the expansion all have different powers of x, and these terms make up the full expansion of the expression.
Remember that the different terms have x raised to different powers. So, to locate the term independent of x (the term which does not contain any x in it, sometimes called the constant term, of which the power of x must be zero), we will have to find the term in which the power of x is zero.
This is done by setting the power of the general term to zero.
4r - 16 = 0
r = 4
This value of r, for the general term, will give us our term independent of x in the expansion.
Different values of r, from r = 0 to r = n, will give us all the different terms in the full expansion, all with different powers of x.
The expansion of any binomial expression is basically the sum of many individual terms in the expansion.
For example, (1 + x)^2 = 1 + 2x + x^2 after simplification. Each of these three individual terms are referred to as individual terms.
A general term is basically a particular term (raised to a power of x) in the full expansion. Sometimes, we wish to know the coefficient of some power of x inside the expansion, but we do not wish to expand out binomially (or worse, manually) because the power is extremely large and the term to find happens to be in the middle.
In such a case, finding out the general term would be more appropriate. Different terms in the expansion all have different powers of x, and these terms make up the full expansion of the expression.
Remember that the different terms have x raised to different powers. So, to locate the term independent of x (the term which does not contain any x in it, sometimes called the constant term, of which the power of x must be zero), we will have to find the term in which the power of x is zero.
This is done by setting the power of the general term to zero.
4r - 16 = 0
r = 4
This value of r, for the general term, will give us our term independent of x in the expansion.
Different values of r, from r = 0 to r = n, will give us all the different terms in the full expansion, all with different powers of x.
So in short, the general term is basically picking out a single term in the expansion rather than fully expanding the expression. The sum of all the general terms in the expansion will give us the full expansion of the expression.
thanks a lot for your help :))
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