Question

The coefficient of x in the expension of (2x-5)³ is *​

Answer 1

Answer:

the answer is 2 in (2x-5)

Answer 2

Answer:

As per binomial theorem:

Consider the expansion:

In general any (k+1)th term in the expansion is given as :

Thus in general the power of x is 18–3k

For the coefficient of x^3 substitute 18–3k=3 yields us k=5

For k=5 we get the term:

Thus only for the expansion the coefficient of x^3 is (-224/27)

However the expansion is multiplied with  1+x+2x2  

Following is the effect of multiplication on the powers of x (one by one):

When the expansion is multiplied with 1, there is no effect on the powers of x

When the entire expansion multiplied with x, all the powers of x in the expansion gets added to 1:

ie:

For  x3  we substitute 19–3k=3 which yields k=5.33 since ‘k’ can take only integer values we wont have  x3  term on multiplying the expansion x.

Similarly on multiplying the expansion with  x2  

In general power of x the becomes 20–3k. for  x3  term substituting 20–3k=3 we get k=5.667 which is again not possible.

Thus we get  x3 only when the expansion is multiplied with 1 and the multiplication  x2  and x wont give any  x3 term. Thus the coefficient of  x3  will remain the same i.e. −224/27

Step-by-step explanation:

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