Question

pls solve the question ​

Answer 1

The coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+x³)⁴ is equal to

the coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+4x³+6x⁶+4x⁹)

We can ignore the last term in the expansion (1+x³)⁴, since its exponent is

greater than 10.

=   Coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³

+4*Coefficient of x⁷ in the expansion of (1+x)²(1+x²)³

+6*Coefficient of x⁴ in the expansion of (1+x)²(1+x²)³

+4*Coefficient of x in the expansion of (1+x)²(1+x²)³,

Coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³ = 0, since the highest degree term in the expansion is 8.

Coefficient of x⁷ in the expansion of (1+x)²(1+x²)³ =

Coefficient of x⁷ in the expansion of (1+2*x+x²)(1+x²)³

= 2*Coefficient of x⁶ in the expansion of (1+x²)³

=2*1 = 2,

Coefficient of x⁴ in the expansion of (1+x)²(1+x²)³ =

Coefficient of x⁴ in the expansion of (1+2*x+x²)(1+x²)³

=1*Coefficient of x⁴ in the expansion of (1+x²)³ +

     1*Coefficient of x in the expansion of (1+x²)³

=3 + 3 =6

Coefficient of x in the expansion of (1+2*x+x²)(1+x²)³

=2* constant in the expansion of (1+x²)³

=2,

Thus ,the coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+x³)⁴

= 0 + 4*2 + 6*6 + 4*2

=52.