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Grade 11Magical Mathematics[Interesting Approach]

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

Lemi Peter

4 Years agoGrade 11

1 Answer

RUSHIKESH RAMESHCHANDRA BENKE

4 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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