Question

preform the multiplication
(5a-3a^3)(4a-1)

Answer 1

To perform the multiplication \((5a - 3a^3)(4a - 1)\), we can use the distributive property (also known as the FOIL method for two binomials).

1. Distribute \(5a\) to both terms in the second binomial:
\[
5a \cdot 4a = 20a^2
\]
\[
5a \cdot (-1) = -5a
\]

2. Distribute \(-3a^3\) to both terms in the second binomial:
\[
-3a^3 \cdot 4a = -12a^4
\]
\[
-3a^3 \cdot (-1) = 3a^3
\]

3. Now, combine all the results:
\[
-12a^4 + 20a^2 + 3a^3 - 5a
\]

4. Rearranging the terms in descending order of degrees gives:
\[
-12a^4 + 3a^3 + 20a^2 - 5a
\]

So the final result of the multiplication \((5a - 3a^3)(4a - 1)\) is:
\[
-12a^4 + 3a^3 + 20a^2 - 5a
\]