Simplify the given algebraic expression: $(3.5e - 4.5f)(1.5e + 4f + ef) - 4.5e + 10f$.

Hint – First multiply the terms given in the first bracket with the terms in the second bracket and then apply simple addition and subtraction to solve.

Complete step-by-step solution -
We have been given $(3.5e - 4.5f)(1.5e + 4f + ef) - 4.5e + 10f$.
Multiplying the two brackets and then adding and subtracting similar terms we get-
$
  (3.5e - 4.5f)(1.5e + 4f + ef) - 4.5e + 10f \\
   = 5.25{e^2} + 14ef + 3.5{e^2}f - 6.75ef - 18{f^2} - 4.5e{f^2} - 4.5e + 10f \\
   = 5.25{e^2} - 18{f^2} + 3.5{e^2}f - 4.5e{f^2} + 7.25ef - 4.5e + 10f \\
$
Therefore, after simplification the answer is –
$(3.5e - 4.5f)(1.5e + 4f + ef) - 4.5e + 10f = 5.25{e^2} - 18{f^2} + 3.5{e^2}f - 4.5e{f^2} + 7.25ef - 4.5e + 10f$.

Note – Whenever simplifying expressions as given in the question, always be careful while multiplying each term of one bracket with other terms of another bracket, as the number of terms is more. So, after multiplying the two bracket terms with each other, add and subtract the similar terms to get the simplified expression.