Question

The coefficient of $x^6$ in the expansion of ${\left(1-x\right)}^8{\left(1+x\right)}^{12}$ is equal to

• A. $168$
• B. $-8$
• C. $28$
• D. $104$

Answer 1

Answer: (D)

${\left(1-x\right)}^8{\left(1+x\right)}^{12}={\left(1-x^2\right)}^8{\left(1+x\right)}^4$
$=\left(1-8x^2+28x^4-56x^6+\dots \right)\left(1+4x+6x^2+4x^3+x^4\right)$
Hence, the coefficient of $x^6=-8+168-56=160=104$