Question

Determine the coefficient of $a^2{b}^{4}d$ in the expansion of the polynomial $(3a+5b-2c+d{)}^7$

• A. $348756$
• B. $493987$
• C. $590625$
• D. $367980$

Answer 1

The correct option is C $590625$

By multinomial theorm, if we need to find the value of expansion

${(x+y+z+w)}^n$ with coefficent $x^{r_1}$.$y^{r_2}$.$z^{r_3}$.$w^{r_4}$, where $r_1+r_2+r_3+r_4$$=n$

So, for ${(3a+5b-2c+d)}^7$ for co-efficient $a^2.b^4.d$.

Thus $\frac{(7!)}{2!.4!.1!}$$3^2{.5}^4.{(-2)}^0{.1}^1$=$105\times 9\times 625\times 1$ $=590625$