Question
Multiply: (6x−5y)(−3x+2y)
(1 point)
Responses
3x−3y
3 x minus 3 y
−31x2y2
negative 31 x squared y squared
−18x2+3xy+10y2
negative 18 x squared plus 3 x y plus 10 y squared
−18x2+27xy−10y2
(1 point)
Responses
3x−3y
3 x minus 3 y
−31x2y2
negative 31 x squared y squared
−18x2+3xy+10y2
negative 18 x squared plus 3 x y plus 10 y squared
−18x2+27xy−10y2
Answers
There are no human answers yet.
Answered by
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).
Let's distribute each term in the first binomial by each term in the second one:
1. First: \(6x \cdot -3x = -18x^2\)
2. Outer: \(6x \cdot 2y = 12xy\)
3. Inner: \(-5y \cdot -3x = 15xy\)
4. Last: \(-5y \cdot 2y = -10y^2\)
Now, add these results together:
\[
-18x^2 + 12xy + 15xy - 10y^2
\]
Combine like terms:
\[
-18x^2 + (12xy + 15xy) - 10y^2 = -18x^2 + 27xy - 10y^2
\]
So, the final answer is:
\[
-18x^2 + 27xy - 10y^2
\]
The correct response is:
\(-18x^2 + 27xy - 10y^2\)
Let's distribute each term in the first binomial by each term in the second one:
1. First: \(6x \cdot -3x = -18x^2\)
2. Outer: \(6x \cdot 2y = 12xy\)
3. Inner: \(-5y \cdot -3x = 15xy\)
4. Last: \(-5y \cdot 2y = -10y^2\)
Now, add these results together:
\[
-18x^2 + 12xy + 15xy - 10y^2
\]
Combine like terms:
\[
-18x^2 + (12xy + 15xy) - 10y^2 = -18x^2 + 27xy - 10y^2
\]
So, the final answer is:
\[
-18x^2 + 27xy - 10y^2
\]
The correct response is:
\(-18x^2 + 27xy - 10y^2\)
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