Try this beautiful problem based on expansion, useful for ISI B.Stat Entrance
The number of terms in the expansion of \([(a+3b)^2 (a-3b)^2]^2\) , when simplified, is
Algebra
multiplication
Expansion
Answer: \(5\)
TOMATO, Problem 102
Challenges and Thrills in Pre College Mathematics
The given expression is \([(a+3b)^2 (a-3b)^2]^2\).we have to find out number of terms in the expansion of \([(a+3b)^2 (a-3b)^2]^2\).
Now , \([(a+3b)^2 (a-3b)^2]^2\) \(\Rightarrow [(a^2-9b^2)^2]^2\) \(\Rightarrow (a^2-9b^2)^4\)
Can you now finish the problem ..........
Now in the equation \((a+b)^2=a^2+2ab+b^2\) i.e total numbers of terms are \(3\)
\((a+b)^3=a^3+3a^2b+3ab^2+b^3\) i.e total numbers of terms are \(4\)
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\((a + b)^n = a^n + { n \choose 1} a^{n-1}b + { n \choose 2 } a^{n-2}b^2 + … + { n \choose {n-1}}ab^{n-1} + b^n\) i.e total numbers of terms are \(n+1\)
Similarly In this expression \((a^2-9b^2)^4\) ,The power is \(4\).Therefore we say that after the expansion total number be \(5\).
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