Final answer:
To simplify the expression 4x(2y) + 3y(2 - x), expand each term and add them together to get the simplified form, which is 8xy + 6y - 3x, making option C the correct answer.
Step-by-step explanation:
The correct answer is option C which is 8xy + 6y - 3x. To simplify the expression 4x(2y) + 3y(2 - x), first expand the terms:
4x × 2y = 8xy (since 4 times 2 equals 8)
3y × 2 = 6y (since 3 times 2 equals 6)
3y × -x = -3xy (sign changes because of the minus)
Adding them together you get: 8xy + 6y - 3xy which simplifies further since there are no like terms with 3xy. Therefore, the expression simplifies to 8xy + 6y - 3x.
The correct answer is option C. 8xy + 6y - 3x.
To simplify the expression, distribute the terms:
4x(2y) = 8xy
3y(2 - x) = 6y - 3xy
Combine like terms:
8xy + 6y - 3xy = 5xy + 6y - 3x
So, the simplified expression is 8xy + 6y - 3x.