Question

The coefficient of $x^4$ in the expansion ${\left(1-x\right)}^8{\left(1+x\right)}^{12}$ is equal to

• A. $1$
• B. $-48$
• C. $28$
• D. $-19$

Answer 1

Answer: (D)

${\left(1-x\right)}^8{\left(1+x\right)}^{12}={\left(1-x^2\right)}^8{\left(1+x\right)}^4$
$=\left(1-8x^2+28x^4\dots .\right)\left(1+4x+6x^2+4x^3+x^4\right)$
Coefficient of $x^4=1-48+28=-19$