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Find the fifth term in the expansion of (2+3/2 x)^8

Find the fifth term in the expansion of (2+3/2 x)^8

Grade:11

1 Answers

RUSHIKESH RAMESHCHANDRA BENKE
15 Points
2 years ago
(2+\frac{3}{2}x)^{8}
We solve this expansion using coeficient triangle
for 1 term                                                                           1
for 2 term                                                                    1     2     1
for 3 term                                                                1     3     3     1
for 4 term                                                             1     4     6     4     1
for 5 term                                                         1     5    10    10    5    1
for 6 term                                                     1     6    15    20   15    6    1
for 7 term                                                 1     7    21    35    35    21   7     1
for 8 term                                            1      8    28    56    70   56    28   8     1
so using coeficient triangle for expansion of 8
The expansion of (2+\frac{3}{2}x)^{8} as follows.
1(2^{8})(\frac{3}{2}x)^{0}+8(2^{7})(\frac{3}{2}x)^{1}+28(2^{6})(\frac{3}{2}x)^{2}+56(2^{5})(\frac{3}{2}x)^{3}+70(2^{4})(\frac{3}{2}x)^{4}+56(2^{3})(\frac{3}{2}x)^{5}+28(2^{2})(\frac{3}{2}x)^{6}+8(2^{1})(\frac{3}{2}x)^{7}+1(2^{0})(\frac{3}{2}x)^{8}
 
So the fifth term is                         70(2^{4})(\frac{3}{2}x)^{4}
 

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