Could someone me on 50? i don’t understand how to use quadratic form with this.

(4x^2 + 1)(2x + 1)(2x - 1)

Step-by-step explanation:

16x^4 - 1

The first rule of factoring is to try to factor a common factor. There is no common factor between 16x^4 and 1.

We see that the polynomial is a binomial. It is a difference of two terms. We also notice that the first term is a perfect square. 16x^4 is the square of 4x^2. 1 is also a perfect square. It is the square of 1. Since both terms are perfect squares, and it is a difference, this binomial is the difference of two squares.

Recall the factoring of the difference of two squares. The difference of two squares factors into the product of a sum and a difference.

The pattern is:

a^2 - b^2 = (a + b)(a - b)

Apply that pattern to our problem. 16x^4 is the square of 4x^2, so the factorization looks like this:

16x^4 - 1 = (4x^2 + 1)(4x^2 - 1)

So far so good, but we are not finished yet. Factoring a polynomial means  factoring it completely. Now we need to look at each factor and see if it can be factored further.

First, look at 4x^2 + 1. 4x^2 is the square of 2x. 1 is the square of 1. This is the sum of two squares. There is no factorization for the sum of two squares, so that factor is done.

Now look at 4x^2 - 1. Again, 4x^2 is the square of 2x, and 1 is the square of 1. In this case, we have the difference of two squares. We use the same factorization pattern we used above, a^2  b^2 = (a + b)(a - b).

16x^4 - 1 = (4x^2 + 1)(2x + 1)(2x - 1)

2x + 1 and 2x - 1 are not factorable, so the fully factored binomial is:

(4x^2 + 1)(2x + 1)(2x - 1)

the answer is 489

step-by-step explanation: