1. The problem is to identify and correct the error in the expression $$(2x - 7)^3 = (2x)^3 - 7^3 = 8x^3 - 343.$$ 2. The error is in the assumption that $$(a - b)^3 = a^3 - b^3.$$ This is incorrect. The correct formula for the cube of a binomial is: $$ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 $$ 3. Applying this formula to $$(2x - 7)^3$$, let $a = 2x$$ and $b = 7$$: $$ (2x - 7)^3 = (2x)^3 - 3(2x)^2(7) + 3(2x)(7)^2 - 7^3 $$ 4. Calculate each term: - $$(2x)^3 = 8x^3$$ - $$3(2x)^2(7) = 3 imes 4x^2 imes 7 = 84x^2$$ - $$3(2x)(7)^2 = 3 imes 2x imes 49 = 294x$$ - $$7^3 = 343$$ 5. Substitute back: $$ (2x - 7)^3 = 8x^3 - 84x^2 + 294x - 343 $$ 6. Therefore, the correct expansion is: $$ (2x - 7)^3 = 8x^3 - 84x^2 + 294x - 343 $$ 7. The original expression incorrectly omitted the middle terms and treated the cube of a difference as the difference of cubes, which is a common mistake. Final answer: $$ (2x - 7)^3 = 8x^3 - 84x^2 + 294x - 343 $$