Question

The number of terms in the expansion of $\left[\right(a+3b{)}^2(a-3b{)}^2{]}^2$ when simplified are :

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is B $5$

The binomial expansion of $(x+y{)}^n$ has $n+1$ terms.

$\Rightarrow$ $\left[\right(a+3b{)}^2(a-3b{)}^2{]}^2={\left[{\left(\right(a{)}^2-\left(3b{)}^2\right)}^2\right]}^2$

$={\left[{(a^2-9b^2)}^2\right]}^2$

$={(a^2-9b^2)}^4$

$\Rightarrow$ $(a^2-9b^2{)}^4$ has $4+1=5$ term.