Answer :

To simplify the given expression [tex]\(3\left[2\left(-y^2 + y\right) - 3\right] - 3(2x + y)\)[/tex], we can follow a step-by-step process:

1. Distribute the constant inside the first set of brackets:

First, consider the inner expression: [tex]\(2(-y^2 + y)\)[/tex].
[tex]\[ 2(-y^2 + y) = 2 \cdot (-y^2) + 2 \cdot y = -2y^2 + 2y \][/tex]

2. Simplify the expression inside the brackets:

Substitute back into the expression within the brackets:
[tex]\[ 2(-y^2 + y) - 3 = -2y^2 + 2y - 3 \][/tex]

3. Distribute the 3 across the simplified expression:

Now distribute the 3:
[tex]\[ 3[-2y^2 + 2y - 3] = 3 \cdot (-2y^2) + 3 \cdot 2y + 3 \cdot (-3) = -6y^2 + 6y - 9 \][/tex]

4. Simplify the second part of the expression:

Distribute the [tex]\(-3\)[/tex] in the second part:
[tex]\[ -3(2x + y) = -3 \cdot 2x - 3 \cdot y = -6x - 3y \][/tex]

5. Combine the simplified parts:

Now add the two parts together:
[tex]\[ -6y^2 + 6y - 9 - 6x - 3y \][/tex]

6. Combine like terms:

Combine the [tex]\(y\)[/tex] terms:
[tex]\[ 6y - 3y = 3y \][/tex]

Thus, the final simplified expression is:
[tex]\[ -6x - 6y^2 + 3y - 9 \][/tex]

Therefore, the fully simplified expression is:
[tex]\[ -6x - 6y^2 + 3y - 9 \][/tex]