Simplify the given algebraic expression: 8 - 9[7 - (3y - 6)].

Step-by-step solution

1. 1

   Work from the innermost bracket outward. With nested brackets there is only one safe order: clear the inside first. Trying to multiply the $-9$ in while $(3y-6)$ is still wrapped up almost always loses a sign.

2. 2

   Remove the inner bracket. The minus sign in front of $(3y-6)$ negates both terms:

   $7 - (3y - 6) = 7 - 3y + 6 = 13 - 3y$

   Note $-(-6) = +6$. Leaving it as $7 - 3y - 6 = 1 - 3y$ is the classic slip.

3. 3

   Rewrite the expression.

   $8 - 9\bigl[\,13 - 3y\,\bigr]$

4. 4

   Distribute $-9$, keeping the minus attached. Treat the coefficient as $-9$, not $9$:

   $-9(13) = -117, \qquad -9(-3y) = +27y$

   so the expression becomes

   $8 - 117 + 27y$

5. 5

   Combine the constants. $8 - 117 = -109$, and there is only one $y$ term:

   $27y - 109$

6. 6

   Check with a test value. At $y = 1$ the original is $8 - 9[7 - (3-6)] = 8 - 9[7 + 3] = 8 - 90 = -82$, and the answer gives $27(1) - 109 = -82$ ✓.