If A denotes the sum of all the coefficients in the expansion of 1 - 3 x + 10 x 2 n and B denotes the sum of…

We have,

$\mathrm{A}=$Sum of the coefficients in the expansion of

$\Rightarrow {\left(1-3x+10x^2\right)}^n=(1-3+10{)}^n=(8{)}^n=(2{)}^{3n}$

(putting $x=1$)

Now, $B=$Sum of the coefficients in the expansion of

$\Rightarrow {\left(1+x^2\right)}^n=(1+1{)}^n=2^n$

Clearly, $A={\mathrm{B}}^3$.