Multiply: (6x−5y)(−3x+2y)

Question

(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

Answer 1

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