Expression Simplification 1Caafc

1. **State the problem:** Simplify the expression $4 (7x^2 + 6x + 6) - 6 (7x^2 + 2x + 6)$ and write it in the form $ax^2 + bx + c$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4 (7x^2 + 6x + 6) = 4 \times 7x^2 + 4 \times 6x + 4 \times 6 = 28x^2 + 24x + 24$$ $$-6 (7x^2 + 2x + 6) = -6 \times 7x^2 - 6 \times 2x - 6 \times 6 = -42x^2 - 12x - 36$$ 3. **Combine like terms:** Add the corresponding coefficients of $x^2$, $x$, and the constant terms. $$28x^2 + 24x + 24 - 42x^2 - 12x - 36 = (28x^2 - 42x^2) + (24x - 12x) + (24 - 36)$$ 4. **Simplify each group:** $$28x^2 - 42x^2 = \cancel{28}x^2 - \cancel{42}x^2 = -14x^2$$ $$24x - 12x = \cancel{24}x - \cancel{12}x = 12x$$ $$24 - 36 = -12$$ 5. **Write the final simplified expression:** $$-14x^2 + 12x - 12$$ **Answer:** The expression equals $-14x^2 + 12x - 12$.