Question

Simplify the following expression.

(−a4−2a3+5)(a2−4a)

(1 point)
Responses

−a6−2a5+4a4+8a3+5a2−20a
negative A to the 6th power minus 2 A to the 5th power plus 4 A to the 4th power plus 8 A cubed plus 5 A squared minus 20 A

−a6+2a5+8a4+5a2−20a
negative A to the 6th power plus 2 A to the 5th power plus 8 A to the 4th power plus 5 A squared minus 20 A

−a6−6a5−8a4+5a2−20a
negative A to the 6th power minus 6 A to the 5th power minus 8 A to the 4th power plus 5 A squared minus 20 A

−a8−2a6+4a4+8a3+5a2−20a

Answer 1

Let's simplify the expression \((−a^4−2a^3+5)(a^2−4a)\).

We will use the distributive property (also known as the FOIL method for binomials):

1. Multiply \(−a^4\) by both terms in the second parentheses:
\[
−a^4 \cdot a^2 = -a^{4+2} = -a^6
\]
\[
−a^4 \cdot (-4a) = 4a^{4+1} = 4a^5
\]

2. Multiply \(−2a^3\) by both terms in the second parentheses:
\[
−2a^3 \cdot a^2 = -2a^{3+2} = -2a^5
\]
\[
−2a^3 \cdot (-4a) = 8a^{3+1} = 8a^4
\]

3. Multiply \(5\) by both terms in the second parentheses:
\[
5 \cdot a^2 = 5a^2
\]
\[
5 \cdot (-4a) = -20a
\]

Now, we can collect all the terms:
\[
-a^6 + 4a^5 - 2a^5 + 8a^4 + 5a^2 - 20a
\]

Next, combine like terms:
- The \(a^5\) terms: \(4a^5 - 2a^5 = 2a^5\)
- There are no other like terms to combine further.

Thus, the final expression becomes:
\[
-a^6 + 2a^5 + 8a^4 + 5a^2 - 20a
\]

Therefore, the simplified expression is:
\[
\boxed{-a^6 + 2a^5 + 8a^4 + 5a^2 - 20a}
\]