Question

(ANSWERED- EASY POINTS!!) 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 ____.

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 ✔ 9x.
The value of b is ✔ 7.
The product of the prime factors is
✔ (9x – 7)(9x + 7).

Answer 1

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^2 = 81x^2 and b^2 = 49. Taking the square root of both sides, we have a = 9x and b = 7.

Therefore, the value of a is 9x and the value of b is 7.

To factor the polynomial completely, we use the formula (a + b)(a - b). Substituting the values of a and b, we have:

(9x + 7)(9x - 7)

The product of the prime factors is (9x - 7)(9x + 7).

I hope this helps!

Answer 2

This equation is a perfect square binomial so you would just square root the front and then square root the back to get (9x+7)(9x-7)

Explanation:

The front is 81x^2 and the back is 49 which are both perfect squares.