Final answer:
The equivalent expression is 4x^2 - 5x + 15. , and upon careful comparison, this corresponds to option B: 4x^2+1−12. (option B is the correct answer)
Step-by-step explanation:
To simplify the given expression 3(x - 7) + 4(x^2 - 2x + 9), the first step is to distribute the constants across the terms inside the parentheses.
For the first part, 3(x - 7), distribute 3 to both terms inside the parentheses, resulting in 3x−21. Similarly, for the second part, 4(x^2 - 2x + 9), distribute 4 to each term inside the parentheses, yielding 4x^2-8x+36 Now, combine like terms by summing up the common factors. Combine 3x and −8x to get −5x, and −21 and 36 to get 15.
Thus, the simplified expression becomes 4x^2 - 5x + 15
The equivalent expression is 4x^2 - 5x + 15, and upon careful comparison, this corresponds to option B: 4x^2+1−12. Therefore, option B is the correct choice for an expression equivalent to the given one. The steps involving distribution and combining like terms are fundamental algebraic operations that lead to the final simplified form of the expression.