Question

The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely. 81x2 – 49 The value of a is . The value of b is . The product of the prime factors is .

Answer 1

To factor the polynomial 81x^2 – 49 completely, you can use the formula a^2 - b^2 = (a + b)(a - b) by setting a = 9x and b = 7. Applying the formula will give you the factorized form as (9x + 7)(9x - 7).

Step-by-step explanation:

The given polynomial, 81x^2 – 49, is a difference of perfect squares. To factor it completely, we can use the formula a^2 - b^2 = (a + b)(a - b). In this case, a is 9x and b is 7. Applying the formula, we can factor 81x^2 – 49 as (9x + 7)(9x - 7).

Answer 2

To answer your question: Rewrite 81x2 as (9x)2.(9x)2−49Rewrite 49 as 72.(9x)2−72 Both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b) where a=9x and b=7.(9x+7)(9x−7)