The fourth term of (2x+y)5 A binomial is a polynomial which contains t

naivlingr 2021-09-08 Answered
The fourth term of (2x+y)5
A binomial is a polynomial which contains two terms. Algebraically, sum or difference of two monomials is a binomial. Binomial theorem is used to expand the binomials to any given power without direct multiplication. According to the theorem, (x+y)n=k=0Ckxnkyk where nCk=C(n,k)=n!(nk)!k! is the binomial coefficient in the theorem. It represents the number of ways in which k unordered outcomes can be selected from a total of n possibilities. The formula to find rth term is given as tr=nCr1xnr+1yr1, where n is the exponent of the binomial, r is the number of the term to be found, x is the first term of the binomial and y is the second term of the binomial.
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Pohanginah
Answered 2021-09-09 Author has 96 answers

Formula used:
The formula to find rth term is given as tr=nCr1xnr+1yr1, where n is the exponent of the exponent of the binomial, r is the number of the term to be found x is the first term of the binomial and y is the second term of the binomial.
Calculation:
Descriptiontr=nCr1xnr+1yr1Step 1: Here we have to assign values as.x=2x and y=yStep 2: We have to find 4th term, that means r=4. For the given problem, n=5. We substitute n and r values to find the 4th termt4=5C41(2x)54+1y41=5C3(2x)2y3t4=5×4×31×2×3(4x2)y3=10(4x2)y3t4=40x2y3
Conclusion: The 4th term of (2x+y)5 is 40x2y3.

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