Question

The coefficient of $x^5$ in the expansion of $(2-x+3x^2{)}^6$ is

• A. 4692
• B. - 4692
• C. 5052
• D. - 5052

Answer 1

The correct option is D

- 5052

$(2-x+3x^2{)}^6{=}^6{C}_0(2-x{)}^6\left(3x^2{)}^0{+}^6{C}_1\right(2-x{)}^5\left(3x^2{)}^1{+}^4{C}_2\right(2-x{)}^4\left(3x^2{)}^2{+}^6{C}_3\right(2-x{)}^3(2x^2{)}^3+...$

Coefficient of $x^{5}is{}^6{C}_0{}^6{C}_{5}2{-}^6{C}_1{}^5{C}_3{2}^2\times 3{-}^6{C}_2{}^4{C}_1{2}^3\times 3^2$

$=-12-6\times 10\times 4\times 3-15\times 4\times 8\times 9$

$=-12-720-4320=-5052$