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# 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

But try the problem first…

Answer: $$5$$

Source

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 $$4$$

………….

………….

$$(a + b)^n = a^n + { n \choose 1} a^{n-1}b + { n \choose 2 } a^{n-2}b^2 + â€¦ + { n \choose {n-1}}ab^{n-1} + b^n$$ 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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