Simplify Expression 2A8373

1. **State the problem:** Simplify the expression $$2 (3x^2 + 7x + 3) - 3 (2x^2 + 6x + 4)$$ and write it in the form $$ax^2 + bx + c$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$2 (3x^2 + 7x + 3) = 2 \times 3x^2 + 2 \times 7x + 2 \times 3 = 6x^2 + 14x + 6$$ $$-3 (2x^2 + 6x + 4) = -3 \times 2x^2 - 3 \times 6x - 3 \times 4 = -6x^2 - 18x - 12$$ 3. **Combine like terms:** $$6x^2 + 14x + 6 - 6x^2 - 18x - 12$$ Group the terms: $$ (6x^2 - 6x^2) + (14x - 18x) + (6 - 12) $$ 4. **Simplify each group:** $$ \cancel{6x^2} - \cancel{6x^2} = 0$$ $$14x - 18x = -4x$$ $$6 - 12 = -6$$ 5. **Final simplified expression:** $$0x^2 - 4x - 6$$ or simply $$-4x - 6$$ **Answer:** The expression equals $$0x^2 - 4x - 6$$, so the coefficients are: $$0$$ for $$x^2$$, $$-4$$ for $$x$$, and $$-6$$ for the constant term.