Simplify the expression (b-2) 3- b (3-b) 2 and find its value when b = 1/3.

To simplify the expression, we open the brackets, for this we use the formula for the cube of the difference (a – b) ^ 3 = a ^ 3 – 3a ^ 2b + 3ab ^ 2 – b ^ 3 and the square of the difference (a – b) ^ 2 = a ^ 2 – 2ab + b ^ 2, and then we multiply the value in front of the brackets by each value in the brackets, and then we give similar terms:

(b – 2) ^ 3 – b * (3 – b) ^ 2 = b ^ 3 – 6b ^ 2 + 12b – 8 – b * (9 – 6b + b ^ 2) = b ^ 3 – 6b ^ 2 + 12b – 8 – 9b + 6b ^ 2 – b ^ 3 = 3b – 8;

b ^ 3 – b ^ 3 = 0;

-6b ^ 2 + 6b ^ 2 = 0;

12b – 9b = 3b.

Find the value of the expression if b = 1/3:

3b – 8 = 3 * 1/3 – 8 = 3/3 – 8 = 1 – 8 = -7.

Answer: -7.