Final answer:
The factored form of the quadratic equation 81x² - 126x + 49 is (9x - 7)², which matches option c.Option C is the correct answer.
Step-by-step explanation:
The factored form of the binomial expansion 81x² - 126x + 49 can be determined by recognizing the pattern of a squared binomial (a - b)² = a² - 2ab + b². We can try to factor this quadratic by looking for two numbers that multiply to 81 (the coefficient of x²) and 49 (the constant term), and also add up to -126 (the coefficient of x). The numbers -63 and -63 fit this pattern since (9x)² = 81x², 2 * 9x * 7 = 126x, and (7)² = 49.
Therefore, the factored form matches the pattern (9x - 7)² and the correct answer is c. (9x - 7)².
The factored form of the given binomial expansion 81x² - 126x + 49 is (9x - 7)².
To factorize the expression, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b). In this case, we have (9x)² - 2(9x)(7) + 7² = (9x - 7)².
Therefore, option c. (9x - 7)² is the correct factored form.