1. **State the problem:** Simplify the expression $$(5x-3)(x+1)-6x+10x^2+(3-5x)^2$$. 2. **Recall formulas and rules:** - Use distributive property: $$(a+b)(c+d) = ac + ad + bc + bd$$. - Square of a binomial: $$(a-b)^2 = a^2 - 2ab + b^2$$. - Combine like terms by adding coefficients of the same powers of $x$. 3. **Expand each term:** - Expand $$(5x-3)(x+1) = 5x \cdot x + 5x \cdot 1 - 3 \cdot x - 3 \cdot 1 = 5x^2 + 5x - 3x - 3 = 5x^2 + 2x - 3$$. - The term $$-6x$$ remains as is. - The term $$10x^2$$ remains as is. - Expand $$(3-5x)^2 = 3^2 - 2 \cdot 3 \cdot 5x + (5x)^2 = 9 - 30x + 25x^2$$. 4. **Combine all expanded terms:** $$5x^2 + 2x - 3 - 6x + 10x^2 + 9 - 30x + 25x^2$$ 5. **Group like terms:** - For $$x^2$$ terms: $$5x^2 + 10x^2 + 25x^2 = 40x^2$$ - For $$x$$ terms: $$2x - 6x - 30x = -34x$$ - For constants: $$-3 + 9 = 6$$ 6. **Write the simplified expression:** $$40x^2 - 34x + 6$$ **Final answer:** $$40x^2 - 34x + 6$$