Multiply: (6x−5y)(−3x+2y)

Question

(1 point)
Responses

−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
negative 18 x squared plus 27 x y minus 10 y squared

3x−3y

Answer 1

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

1. Multiply the first terms: \(6x \cdot -3x = -18x^2\)
2. Multiply the outer terms: \(6x \cdot 2y = 12xy\)
3. Multiply the inner terms: \(-5y \cdot -3x = 15xy\)
4. Multiply the last terms: \(-5y \cdot 2y = -10y^2\)

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

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

Thus, the final result is: \[ -18x^2 + 27xy - 10y^2 \]

So, the correct answer from the options provided is: −18x² + 27xy − 10y² (negative 18 x squared plus 27 x y minus 10 y squared).