Factor completely.
b Superscript 4 Baseline minus 1
Question content area bottom
Part 1
b Superscript 4 Baseline minus 1equals
  
enter your response here
​(Factor completely. Simplify your​ answer.)

The expression \( b^4 - 1 \) is a difference of squares, which can be factored as follows:

\[
b^4 - 1 = (b^2)^2 - 1^2
\]

Using the difference of squares formula:

\[
a^2 - b^2 = (a - b)(a + b)
\]

we get:

\[
b^4 - 1 = (b^2 - 1)(b^2 + 1)
\]

Now, the term \( b^2 - 1 \) is also a difference of squares, and can be factored further:

\[
b^2 - 1 = (b - 1)(b + 1)
\]

So the complete factorization is:

\[
b^4 - 1 = (b - 1)(b + 1)(b^2 + 1)
\]

### Final answer:
\[
b^4 - 1 = (b - 1)(b + 1)(b^2 + 1)
\]

Would you like further clarification on any step?

### Related questions:
1. How do you factor higher powers of binomials?
2. What is the difference between sum of squares and difference of squares?
3. Can the expression \( b^4 + 1 \) be factored?
4. How do you factor trinomials like \( b^2 + b + 1 \)?
5. What is the general process for factoring polynomials completely?

### Tip:
Always check if the expression is a perfect square, a difference of squares, or can be factored further after applying common factoring formulas.

Learn how to factor b^4 - 1 completely using the difference of squares method. This problem covers key algebraic concepts such as factoring higher powers and applying the difference of squares formula. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation