Question

Write your answer in descending powers of a (a^3 - 2a + 5) - (4a^3 - 5a^2 + a - 2)

Answer 1

Given the expression below

`\left(a^3-2a+5\right)-\left(4a^3-5a^2+\:a-2\right)`

Evaluating the expression gives

`\begin{gathered} =a^3-2a+5-4a^3+5a^2-a+2 \\ Collect\text{ like terms} \\ =a^3-4a^3+5a^2-2a-a+5+2 \\ =-3a^3+5a^2-3a+7 \end{gathered}`

Hence, the answer is

`\begin{equation*} -3a^3+5a^2-3a+7 \end{equation*}`