Question

The coefficient of $x^{10}$ in the expansion of$(1+x{)}^2{(1+x^2)}^3{(1+x^3)}^4$ is equal to:

• A. $52$
• B. $56$
• C. $50$
• D. $44$

Answer 1

The correct option is A $52$

$(1+x^2)(1+x^2{)}^3(1+x^3{)}^4$

$(1+x^2)(1+x^6+3x^2+3x^4)\left(1{+}^4{C}_1{x}^3{+}^4{C}_2{x}^6{+}^4{C}_3{x}^9{+}^4{C}_4{x}^{12}\right)$

Using Binomial expansion

Take $x^{10}$ coefficient from multiplication

$2[3{\times }^4{C}_2+3{\times }^4{C}_2]$

$=52$