Question

Expand the expression to a polynomial in standard form:
left parenthesis, minus, 3, x, plus, 1, right parenthesis, left parenthesis, minus, 2, x, squared, plus, 5, x, plus, 5, right parenthesis
(−3x+1)(−2x
2
+5x+5)

Answer 1

To expand the expression \((−3x+1)(−2x^2+5x+5)\), we can use the distributive property (also known as the FOIL method).

1. Distribute \(-3x\) to each term in \(-2x^2 + 5x + 5\):

\[
-3x \cdot (-2x^2) = 6x^3
\]
\[
-3x \cdot 5x = -15x^2
\]
\[
-3x \cdot 5 = -15x
\]

2. Now distribute \(1\) to each term in \(-2x^2 + 5x + 5\):

\[
1 \cdot (-2x^2) = -2x^2
\]
\[
1 \cdot 5x = 5x
\]
\[
1 \cdot 5 = 5
\]

3. Combine all the results:

\[
6x^3 - 15x^2 - 15x - 2x^2 + 5x + 5
\]

4. Now, combine like terms:

- For \(x^2\) terms: \(-15x^2 - 2x^2 = -17x^2\)
- For \(x\) terms: \(-15x + 5x = -10x\)

So the combined expression becomes:

\[
6x^3 - 17x^2 - 10x + 5
\]

Thus, the expanded expression in standard form is:

\[
\boxed{6x^3 - 17x^2 - 10x + 5}
\]