Question

the coefficient of x^7in(1-x+x^2+x^3)^6 is​

Answer 1

Answer:

Step-by-step explanation

The coefficient of x^7 is -144

Hope this is helpful to you

Answer 2

Answer:

here is your answer

Step-by-step explanation:

(1−x−x2+x3)6=((1−x)(1−x2))6(1−x−x2+x3)6=((1−x)(1−x2))6

=(1−x)12.(1+x)6=(1−x)12.(1+x)6

Coefficient of xnxn in (1+x)6(1+x)6 = 6Cn6Cn

Coefficient of xnxn in (1−x)12(1−x)12 = (−1)n(−1)n.12Cn12Cn

Coeff. of x7x7 in this expansion =

coeff. of xx in (1−x)12(1−x)12.coeff of x6x6 in (1+x)6+(1+x)6+

coeff. of x2x2 in (1−x)12(1−x)12.coeff of x5x5 in (1+x)6+(1+x)6+

coeff. of x3x3 in (1−x)12(1−x)12.coeff of x4x4 in (1+x)6+(1+x)6+

coeff. of x4x4 in (1−x)12(1−x)12.coeff of x3x3 in (1+x)6+(1+x)6+

coeff. of x5x5 in (1−x)12(1−x)12.coeff of x2x2 in (1+x)6+(1+x)6+

coeff. of x6x6 in (1−x)12(1−x)12.coeff of xx in (1+x)6+(1+x)6+

coeff. of x7x7 in (1−x)12(1−x)12.coeff of x0x0 in (1+x)6+(1+x)6+

=

−(12C1.6C6)+(12C2.6C5)−(12C3.6C4)+(12C4.6C3)−(12C1.6C6)+(12C2.6C5)−(12C3.6C4)+(12C4.6C3)

−(12C5.6C2)+(12C6.6C1)−(12C7.6C0)−(12C5.6C2)+(12C6.6C1)−(12C7.6C0)

=−12+(66×6)−(220×15)+(495×20)−(792×15)+(132×42)−792=−12+(66×6)−(220×15)+(495×20)−(792×15)+(132×42)−792

=−144=−144