Math Problem Statement

Find the continued product of (x - 1)(x^2 + 1).

Solution

The question asks to find the "continued product" of the given expression (x1)(x2+1)(x - 1)(x^2 + 1).

Solution:

  1. Expand the expression (x1)(x2+1)(x - 1)(x^2 + 1) using the distributive property: (x1)(x2+1)=x(x2+1)1(x2+1)(x - 1)(x^2 + 1) = x(x^2 + 1) - 1(x^2 + 1)

  2. Simplify each term: x(x2+1)=x3+xx(x^2 + 1) = x^3 + x 1(x2+1)=x21-1(x^2 + 1) = -x^2 - 1

  3. Combine all terms: x3+xx21x^3 + x - x^2 - 1

  4. Rearrange in standard polynomial form: x3x2+x1x^3 - x^2 + x - 1

Final Answer:

The expanded product is: x3x2+x1x^3 - x^2 + x - 1

Would you like further clarification or examples?

Related Questions:

  1. What is the continued product of (x+2)(x23)(x + 2)(x^2 - 3)?
  2. How can you verify the result of a polynomial multiplication?
  3. What are the steps for expanding (ab)(c+d)(a - b)(c + d)?
  4. What is the degree of the resulting polynomial in this question?
  5. How does the distributive property help in polynomial multiplication?

Tip:

When expanding products of polynomials, ensure each term in the first polynomial multiplies with every term in the second.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Polynomial Multiplication
Algebra
Distributive Property

Formulas

(a + b)(c + d) = ac + ad + bc + bd

Theorems

Distributive Property of Multiplication over Addition

Suitable Grade Level

Grade 7