1. **State the problem:** Simplify the expression $$6x^2 - (2x - 1)(2x - 5) - 2x(x + 3)$$. 2. **Recall formulas and rules:** - Use the distributive property to expand products: $ (a - b)(c - d) = ac - ad - bc + bd $. - Combine like terms after expansion. 3. **Expand the product $(2x - 1)(2x - 5)$:** $$ (2x - 1)(2x - 5) = 2x \cdot 2x - 2x \cdot 5 - 1 \cdot 2x + 1 \cdot 5 = 4x^2 - 10x - 2x + 5 = 4x^2 - 12x + 5 $$ 4. **Expand the product $2x(x + 3)$:** $$ 2x(x + 3) = 2x \cdot x + 2x \cdot 3 = 2x^2 + 6x $$ 5. **Rewrite the original expression with expansions:** $$ 6x^2 - (4x^2 - 12x + 5) - (2x^2 + 6x) $$ 6. **Distribute the minus signs:** $$ 6x^2 - 4x^2 + 12x - 5 - 2x^2 - 6x $$ 7. **Combine like terms:** - For $x^2$ terms: $6x^2 - 4x^2 - 2x^2 = \cancel{6x^2} - \cancel{4x^2} - 2x^2 = 0x^2$ - For $x$ terms: $12x - 6x = 6x$ - Constant term: $-5$ 8. **Final simplified expression:** $$ 6x - 5 $$ **Answer:** $6x - 5$