Question

The number of terms in the expansion of $(1+5\sqrt{2}x{)}^9+(1-5\sqrt{2}x{)}^9$ is

• A. 5
• B. 7
• C. 9
• D. 10

Answer 1

The correct option is A 5

$S=(1+5\sqrt{2}x{)}^9+(1-5\sqrt{2}x{)}^9$
Let $k=5\sqrt{2}$
Then the above binomial expansion changes to
$S=(1+k{)}^9+(1-k{)}^9$
$=[1+{}^9{C}_{1}k+{}^9{C}_2{k}^2+...{}^9{C}_9{k}^9]+[1-{}^9{C}_{1}k+{}^9{C}_2{k}^2-{}^9{C}_3{k}^3...-{}^9{C}_9{k}^9]$
$=2[1+{}^9{C}_2{k}^2+{}^9{C}_4{k}^4+{}^9{C}_6{k}^6+{}^9{C}_8{k}^8]$
Hence in total 5 terms will be there.