In Exercises 83–94, find each product.(x + 1)(x − 1)(x² + 1)

Question

Accepted Answer

Hello, today we're gonna be performing multiplication on the given expression. So what we are given is the quantity M plus one times M minus one times M squared plus one. Now, the quantity M squared plus one is already in its simplest form. So for now we're going to leave this quantity by itself, but we can go ahead and simplify M plus one times M minus one. And we can do this by using the difference of squares, see the difference of square states that if you have a binomial in the form of A squared minus B squared, this can be factored to give us the quantities A plus B Times A. -7. And here M plus one times M minus one matches the right hand side of the difference of squares. So we're going to use the difference of squares, but we're gonna be using the property going from right to left and we're gonna be using it to simplify the two quantities M plus one times M minus one. Here, we're going to allow A to equal to M and we're going to allow B to equal to one. So we can rewrite the first two quantities as M squared minus one squared. And on the left hand side, we can rewrite this without the parentheses to give us M squared. And one race to any power is just going to give us one. So we have M squared minus one. Now keep in mind, we still have to include that same quantity from the beginning M squared plus one. So we have M squared minus one times M squared plus one. And if there's one thing that you notice about this M squared minus one times M squared plus one also matches the right hand side of the difference of squares. So we can apply the difference of squares again to these two quantities. But here we're going to allow A to equal to M squared. And we're going to allow B to equal to one and using the difference of squares one more time, we can rewrite the S quantity as M squared race the power of two minus one squared. Now, on the left hand side, we can use our exponential multiplication to multiply the two exponents together. So we get M squared times two, which is going to give us M to the power of four. And on the right hand side, one race to any power is just going to give us one. So we have M to the power of 4 -1. And this is going to be the simplified form of the original expression. And with that being said, the answer to this problem is going to be d so I hope this video helps you in understanding how to approach this problem. And we'll go ahead and see you all in the next video.

In Exercises 83–94, find each product.(x + 1)(x − 1)(x² + 1)

Key Concepts

Factoring and Expanding Polynomials

Difference of Squares

Polynomial Multiplication

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