i cant seem to get the answer that the teacher gave us which is 5y^2-11y

2y^2-y(3-2(y-4)-y)

Get rid of the inner brackets:

2y^2 - y(3 - 2y + 8 -y)

Multiply the y into the brackets:

2y^2 - (3y - 2y^2 + 8y - y^2)

2y^2 - 3y + 2y^2 - 8y + y^2

Now collect the terms together.

Thanks

You're welcome!

To simplify the expression 2y^2 - y[3 - 2(y - 4) - y], we will follow the order of operations, which is commonly referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Let's break it down step by step:

Step 1: Simplify the expression inside the square brackets [ ]:
Inside the square brackets [ ], there is a subtraction operation (3 - 2(y - 4) - y).
To simplify this, apply the distributive property by multiplying -2 to both y and -4:
3 - 2y + 8 - y

Combine like terms:
(3 + 8) - (2y + y)
11 - 3y

Step 2: Expand the expression by distributing y in front of the square brackets [ ]:
2y^2 - y(11 - 3y)

Apply the distributive property again:
2y^2 - 11y + 3y^2

Step 3: Combine like terms:
2y^2 + 3y^2 - 11y

Step 4: Simplify further:
5y^2 - 11y

So the final answer is 5y^2 - 11y.