Question

Multiply: (6x−5y)(−3x+2y)
(1 point)
Responses

3x−3y

−18x^2+27xy−10y^2

−18x^2+3xy+10y^2

−31x^2y^2

Answer 1

To multiply the two binomials \((6x−5y)(−3x+2y)\), we can use the distributive property (also known as the FOIL method for binomials).

1. **First:** Multiply the first terms:
\[
6x \cdot -3x = -18x^2
\]

2. **Outer:** Multiply the outer terms:
\[
6x \cdot 2y = 12xy
\]

3. **Inner:** Multiply the inner terms:
\[
-5y \cdot -3x = 15xy
\]

4. **Last:** Multiply the last terms:
\[
-5y \cdot 2y = -10y^2
\]

Now, combine all the results:
\[
-18x^2 + 12xy + 15xy - 10y^2
\]

Combine the like terms \(12xy\) and \(15xy\):
\[
-18x^2 + 27xy - 10y^2
\]

Thus, the final answer is:
\[
\boxed{-18x^2 + 27xy - 10y^2}
\]