Question

The constant term in the expansion of $[1-(x-2{)}^2{]}^{10}$ is equal to :

• A. $2^{10}$
• B. $6^{10}$
• C. $4^{10}$
• D. $5^{10}$
• E. $3^{10}$

Answer 1

The correct option is E $3^{10}$

We know $[1-(x-2{)}^2{]}^{10}=[1-(x^2-4x+4){]}^{10}$
$=[-3-(x^2-4x){]}^{10}$
$=(-1{)}^{10}[3+(x^2-4x){]}^{10}$
$=[3+(x^2-4x){]}^{10}$
Therefore, the general term is $r_{r+1}{=}^{10}{C}_r{3}^{10-r}(x^2-4x{)}^r$.
For constant term, put $r=0$
Hence, the constant term is $3^{10}.$