1. **State the problem:** Simplify the expression $$(3x+4)(3x+4)(7x-1)$$. 2. **Rewrite the expression:** Notice that $$(3x+4)(3x+4) = (3x+4)^2$$, so the expression becomes $$(3x+4)^2(7x-1)$$. 3. **Expand the square:** Use the formula $$(a+b)^2 = a^2 + 2ab + b^2$$ with $a=3x$ and $b=4$: $$ (3x+4)^2 = (3x)^2 + 2 \cdot 3x \cdot 4 + 4^2 = 9x^2 + 24x + 16 $$ 4. **Substitute back:** Now the expression is: $$ (9x^2 + 24x + 16)(7x - 1) $$ 5. **Multiply the polynomials:** Distribute each term in the first polynomial by each term in the second: $$ 9x^2 \cdot 7x = 63x^3 $$ $$ 9x^2 \cdot (-1) = -9x^2 $$ $$ 24x \cdot 7x = 168x^2 $$ $$ 24x \cdot (-1) = -24x $$ $$ 16 \cdot 7x = 112x $$ $$ 16 \cdot (-1) = -16 $$ 6. **Combine like terms:** $$ 63x^3 + (-9x^2 + 168x^2) + (-24x + 112x) - 16 = 63x^3 + 159x^2 + 88x - 16 $$ 7. **Final simplified expression:** $$ \boxed{63x^3 + 159x^2 + 88x - 16} $$