Question

The number of terms in the expansion of $\left[\right(x-3y{)}^2(x+3y{)}^2{]}^3$ is

• A. $6$
• B. $7$
• C. $8$
• D. $Noneofthese$

Answer 1

The correct option is A $6$

${\left[{(x-3y)}^2{(x+3y)}^2\right]}^2$

$={\left[(x-3y)(x-3y)(x+3y)(x+3y)\right]}^2$

$={\left[(x-3y)(x+3y)(x-3y)(x+3y)\right]}^2$

$={\left[{(x^2-9y^2)}^2\right]}^2$ ...... $\because a^2-b^2=(a-b)(a+b)$

$={(x^2+81y^2-18x^2{y}^2)}^2$

We know, $(a+b+c{)}^2=a^2+b^2+c^2+2ab+2ac+2bc$

$=x^4+6,561y^4+324x^4{y}^4+162x^2{y}^2-2,916‬x^2{y}^4-36x^4{y}^2$

$\therefore$Total number of terms$=6$