Question

Find the 5th term in the Binomial expansion of:
(a) (x+3y)7​

Answer 1

Answer:

7x+21y

Step-by-step explanation:

7*x+3y*x

7x+21y

Answer 2

We need to recall the Binomial expansion formula.

• $(x+y)^n=\sum_{r=0}^n {^nC_r} x^{n-r}y^r$

This problem is about the Binomial expansion.

Given:

$(x+3y)^7$

Using the Binomial expansion formula, we get$(x+3y)^7= {^7C_0} x^{7}+{^7C_1} x^{6}(3y)+{^7C_2} x^{7-2}(3y)^2+{^7C_3} x^{7-3}(3y)^3+{^7C_4} x^{7-4}(3y)^4+{^7C_5} x^{7-5}(3y)^5+{^7C_6} x^{7-6}(3y)^6+{^7C_7} x^{7-7}(3y)^7$

$(x+3y)^7= x^{7}+7 x^{6}(3y)+21x^{5}(9y^2)+35 x^4(27y^3)+35 x^{3}(81y^4)+21 x^{2}(243y^5)+7x(729y^6)+2187y^7$

$(x+3y)^7= x^{7}+21 x^{6}y+189x^{5}y^2+945 x^4y^3+2835 x^{3}y^4+5103 x^{2}y^5+5103xy^6+2187y^7$

Hence, the fifth term of the expansion is $2835x^3y^4$.