Try this beautiful problem based on expansion, useful for ISI B.Stat Entrance

Expansion Problem | ISI B.Stat TOMATO 102


The number of terms in the expansion of \([(a+3b)^2 (a-3b)^2]^2\) , when simplified, is

  • 4
  • 5
  • 6
  • 7

Key Concepts


Algebra

multiplication

Expansion

Check the Answer


But try the problem first…

Answer: \(5\)

Source
Suggested Reading

TOMATO, Problem 102

Challenges and Thrills in Pre College Mathematics

Try with Hints


First hint

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 ……….

Second Hint

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 \(4\)

………….

………….

\((a + b)^n = a^n + { n \choose 1} a^{n-1}b + { n \choose 2 } a^{n-2}b^2 + … + { n \choose {n-1}}ab^{n-1} + b^n\) 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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