Question
Multiply: (6x−5y)(−3x+2y)
(1 point)
Responses
3x−3y
3 x minus 3 y
−18x2+27xy−10y2
negative 18 x squared plus 27 x y minus 10 y squared
−31x2y2
negative 31 x squared y squared
−18x2+3xy+10y2
(1 point)
Responses
3x−3y
3 x minus 3 y
−18x2+27xy−10y2
negative 18 x squared plus 27 x y minus 10 y squared
−31x2y2
negative 31 x squared y squared
−18x2+3xy+10y2
Answers
GPT-4o mini
To multiply the expressions \( (6x - 5y)(-3x + 2y) \), we can use the distributive property (also known as the FOIL method for binomials). Here’s the step-by-step calculation:
1. **First Terms**: \( 6x \cdot -3x = -18x^2 \)
2. **Outer Terms**: \( 6x \cdot 2y = 12xy \)
3. **Inner Terms**: \( -5y \cdot -3x = 15xy \)
4. **Last Terms**: \( -5y \cdot 2y = -10y^2 \)
Now, combine all these results:
\[
-18x^2 + 12xy + 15xy - 10y^2
\]
Combine the like terms (the \( xy \) terms):
\[
-18x^2 + (12xy + 15xy) - 10y^2 = -18x^2 + 27xy - 10y^2
\]
So the final result is:
\[
-18x^2 + 27xy - 10y^2
\]
The correct response is:
**−18x² + 27xy − 10y²**
So, the correct option from your responses is:
**−18x² + 27xy − 10y²**
1. **First Terms**: \( 6x \cdot -3x = -18x^2 \)
2. **Outer Terms**: \( 6x \cdot 2y = 12xy \)
3. **Inner Terms**: \( -5y \cdot -3x = 15xy \)
4. **Last Terms**: \( -5y \cdot 2y = -10y^2 \)
Now, combine all these results:
\[
-18x^2 + 12xy + 15xy - 10y^2
\]
Combine the like terms (the \( xy \) terms):
\[
-18x^2 + (12xy + 15xy) - 10y^2 = -18x^2 + 27xy - 10y^2
\]
So the final result is:
\[
-18x^2 + 27xy - 10y^2
\]
The correct response is:
**−18x² + 27xy − 10y²**
So, the correct option from your responses is:
**−18x² + 27xy − 10y²**