Final answer:
To multiply the binomials (-6x+6) and (4x-5y-2), each term in the first binomial is multiplied by each term in the second binomial, and like terms are collected to give the final expression -24x^2 + 30xy + 36x - 30y - 12.
Step-by-step explanation:
The student is asked to multiply the binomials (-6x+6) and (4x-5y-2) and then to collect like terms. To do this, we will use the distributive property to multiply each term in the first binomial by each term in the second binomial.
Multiply -6x by 4x: (-6x)*(4x) = -24x2
- Multiply -6x by -5y: (-6x)*(-5y) = 30xy (because when two negative numbers multiply, the answer has a +ve sign)
- Multiply -6x by -2: (-6x)*(-2) = 12x
- Multiply 6 by 4x: 6*(4x) = 24x
- Multiply 6 by -5y: 6*(-5y) = -30y
- Multiply 6 by -2: 6*(-2) = -12
Adding these up, we get:
-24x2 + 30xy + 12x + 24x - 30y - 12
Now, combine like terms:
- Combine 12x and 24x: 12x + 24x = 36x
So, the final simplified expression is:
-24x2 + 30xy + 36x - 30y - 12