Question

Multiply (6x - 5y) (-3x + 2y)

Answer 1

To multiply the expressions \((6x - 5y)\) and \((-3x + 2y)\), we will use the distributive property (also known as the FOIL method for binomials):

\[
(6x - 5y)(-3x + 2y)
\]

We will multiply each term in the first expression by each term in the second expression:

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 together:

\[
-18x^2 + 12xy + 15xy - 10y^2
\]

Next, we can combine the like terms (\(12xy\) and \(15xy\)):

\[
-18x^2 + (12xy + 15xy) - 10y^2 = -18x^2 + 27xy - 10y^2
\]

Thus, the final result is:

\[
\boxed{-18x^2 + 27xy - 10y^2}
\]