Mathematics Notes | EduRev

Algebra for IIT JAM Mathematics

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Mathematics : Mathematics Notes | EduRev

The document Mathematics Notes | EduRev is a part of the Mathematics Course Algebra for IIT JAM Mathematics.
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For problems 1 & 2 use the Binomial Theorem to expand the given function.

1. Use the Binomial Theorem to expand (4+3x)5.

Solution. Not really a lot to do with this problem.  All we need to do is use the formula from the Binomial Theorem to do the expansion.  Here is that work. 

 Mathematics Notes | EduRev

2. Use the Binomial Theorem to expand (9−x)4.

Solution. Not really a lot to do with this problem.  All we need to do is use the formula from the Binomial Theorem to do the expansion.  Here is that work.

 Mathematics Notes | EduRev

3. Write down the first four terms in the binomial series for (1+3x)−6.

Solution. First, we need to make sure it is in the proper form to use the Binomial Series from the notes which in this case we are already in the proper form with k = -6.

Step 2. Now all we need to do is plug into the formula from the notes and write down the first four terms.

 Mathematics Notes | EduRev

4. Write down the first four terms in the binomial series for 3√8−2x.

Solution. First, we need to make sure it is in the proper form to use the Binomial Series.  Here is the proper form for this function, 

 Mathematics Notes | EduRev

Recall that for proper from we need it to be in the form “1+” and so we needed to factor the 8 out of the root and “move” the minus sign into the second term.  Also, as we can see we will have  Mathematics Notes | EduRev

Step 2. Now all we need to do is plug into the formula from the notes and write down the first four terms. 

 Mathematics Notes | EduRev

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