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I.S.I. and C.M.I. Entrance

Expansion Problem | ISI B.Stat Objective | TOMATO 102

Try this beautiful problem based on expansion from TOMATO 102 useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

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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