Question
18 of 2018 of 20 Items
Question
Multiply:
(x2−1)(−2x+5)
(1 point)
Responses
2x3+5x2+2x−5
2 x cubed plus 5 x squared plus 2 x minus 5
−2x3−5x2−2x+5
negative 2 x cubed minus 5 x squared minus 2 x plus 5
−2x3+5x2+2x−5
negative 2 x cubed plus 5 x squared plus 2 x minus 5
x2−2x+4
Question
Multiply:
(x2−1)(−2x+5)
(1 point)
Responses
2x3+5x2+2x−5
2 x cubed plus 5 x squared plus 2 x minus 5
−2x3−5x2−2x+5
negative 2 x cubed minus 5 x squared minus 2 x plus 5
−2x3+5x2+2x−5
negative 2 x cubed plus 5 x squared plus 2 x minus 5
x2−2x+4
Answers
GPT-4o mini
To multiply the expressions \((x^2 - 1)(-2x + 5)\), you can use the distributive property (also known as the FOIL method for binomials).
Here’s how you do it step-by-step:
1. Distribute \(-2x\) to both terms in \((x^2 - 1)\):
\[
-2x \cdot x^2 = -2x^3
\]
\[
-2x \cdot (-1) = 2x
\]
2. Distribute \(5\) to both terms in \((x^2 - 1)\):
\[
5 \cdot x^2 = 5x^2
\]
\[
5 \cdot (-1) = -5
\]
3. Combine all the results:
\[
-2x^3 + 5x^2 + 2x - 5
\]
So, the result of multiplying \((x^2 - 1)(-2x + 5)\) is:
\[
-2x^3 + 5x^2 + 2x - 5
\]
Thus, the correct response is:
**−2x³ + 5x² + 2x − 5** (negative 2 x cubed plus 5 x squared plus 2 x minus 5).
Here’s how you do it step-by-step:
1. Distribute \(-2x\) to both terms in \((x^2 - 1)\):
\[
-2x \cdot x^2 = -2x^3
\]
\[
-2x \cdot (-1) = 2x
\]
2. Distribute \(5\) to both terms in \((x^2 - 1)\):
\[
5 \cdot x^2 = 5x^2
\]
\[
5 \cdot (-1) = -5
\]
3. Combine all the results:
\[
-2x^3 + 5x^2 + 2x - 5
\]
So, the result of multiplying \((x^2 - 1)(-2x + 5)\) is:
\[
-2x^3 + 5x^2 + 2x - 5
\]
Thus, the correct response is:
**−2x³ + 5x² + 2x − 5** (negative 2 x cubed plus 5 x squared plus 2 x minus 5).