The value of ( 4.6 )^4 + ( 5.4 )^4 + ( 24.84 )^2 ( 4.6 )^2 + ( 5.4 )^2 + 24.84 is:

Answer: Option B

$$\begin{array}{rl}& 4.6=b\\ & 5.4=a\\ & \frac{b^4+a^4+a^2{b}^2}{a^2+b^2+ab}\\ & =\frac{\left(a^2+b^2+ab\right)\left(a^2+b^2-ab\right)}{a^2+b^2+ab}\\ & =a^2+b^2-ab\\ & ={\left(a-b\right)}^2+ab\\ & ={\left(5.4-4.6\right)}^2+24.84\\ & =0.8^2+24.84\\ & =25.48\end{array}$$