1. The problem asks to find the value of the constant $B$ in the expression $$6(x - 3)^2 = Ax^2 + Bx + C.$$ 2. First, expand the left side using the binomial expansion formula $ (x - 3)^2 = x^2 - 2 \times 3 \times x + 3^2 = x^2 - 6x + 9 $. 3. Multiply the entire expansion by 6: $$6(x - 3)^2 = 6(x^2 - 6x + 9) = 6x^2 - 36x + 54.$$ 4. Now, compare this with the right side: $$Ax^2 + Bx + C = 6x^2 - 36x + 54.$$ 5. By matching coefficients of like terms, we get: - $A = 6$ - $B = -36$ - $C = 54$ 6. Therefore, the value of $B$ is **$-36$**.