1. **State the problem:** Expand the function $$f(x) = (7x - 2)^3$$ into the form $$ax^3 + bx^2 + cx + d$$ where $a,b,c,d$ are constants. 2. **Formula used:** Use the binomial expansion formula for cubes: $$ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 $$ 3. **Apply the formula:** Here, $a = 7x$ and $b = 2$. Calculate each term: - $a^3 = (7x)^3 = 7^3 x^3 = 343x^3$ - $3a^2b = 3 \times (7x)^2 \times 2 = 3 \times 49x^2 \times 2 = 294x^2$ - $3ab^2 = 3 \times 7x \times 2^2 = 3 \times 7x \times 4 = 84x$ - $b^3 = 2^3 = 8$ 4. **Put it all together:** $$ (7x - 2)^3 = 343x^3 - 294x^2 + 84x - 8 $$ 5. **Final answer:** $$f(x) = 343x^3 - 294x^2 + 84x - 8$$