Multiply: (6x−5y)(−3x+2y)

Question

(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

Answer 1

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:

\(-18x^2 + 27xy - 10y^2\)