To expand the expression \((x + 1)(x - 4)(x + 5)\), we'll multiply the factors step by step.

### Step 1: Expand the first two factors
\[
(x + 1)(x - 4) = x(x - 4) + 1(x - 4) = x^2 - 4x + x - 4 = x^2 - 3x - 4
\]

### Step 2: Multiply the result by the third factor
Now, multiply \((x^2 - 3x - 4)\) by \((x + 5)\):
\[
(x^2 - 3x - 4)(x + 5) = x^2(x + 5) - 3x(x + 5) - 4(x + 5)
\]
Expand each term:
\[
= x^3 + 5x^2 - 3x^2 - 15x - 4x - 20
\]
Combine like terms:
\[
= x^3 + 2x^2 - 19x - 20
\]

So, the expanded form of \((x + 1)(x - 4)(x + 5)\) is:
\[
\boxed{x^3 + 2x^2 - 19x - 20}
\]

Would you like more details on this expansion, or do you have any questions?

---

Here are some related questions:
1. How do you factor a cubic polynomial like \(x^3 + 2x^2 - 19x - 20\)?
2. What is the process for multiplying three binomials in general?
3. How do you identify the roots of a cubic equation given in standard form?
4. What are the applications of cubic polynomials in real-world problems?
5. Can synthetic division be used to simplify the expansion of cubic polynomials?

**Tip:** When expanding multiple binomials, it's often easier to start by expanding two at a time, then multiply the result by the next factor.

Learn how to expand the expression (x + 1)(x - 4)(x + 5) step-by-step with a detailed solution. This problem covers key algebraic concepts, including polynomial multiplication and binomial expansion formula. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation