(t-s)(X)     (-×²+×+6)-(×³+2×²-4×-8

It seems like you're dealing with an algebraic expression. The expression you've provided is:

\[
(t-s)(X) \quad \text{and} \quad (-x^2 + x + 6) - (x^3 + 2x^2 - 4x - 8)
\]

Let's first clarify the terms involved:

1. The first part, \((t-s)(X)\), looks like a multiplication of the binomial \((t-s)\) with some value \(X\).
2. The second part is a subtraction between two polynomials: \(-x^2 + x + 6\) and \(x^3 + 2x^2 - 4x - 8\).

Let's start by simplifying the subtraction of the polynomials:

\[
(-x^2 + x + 6) - (x^3 + 2x^2 - 4x - 8)
\]

Distribute the negative sign across the second polynomial:

\[
-x^2 + x + 6 - x^3 - 2x^2 + 4x + 8
\]

Now, combine like terms:

\[
(-x^3) + (-x^2 - 2x^2) + (x + 4x) + (6 + 8)
\]

Simplifying each group:

\[
-x^3 - 3x^2 + 5x + 14
\]

So, the simplified polynomial after subtraction is:

\[
-x^3 - 3x^2 + 5x + 14
\]

Now, let's incorporate the first part, \((t-s)(X)\). If you meant to multiply this expression by the simplified polynomial, then the final expression would look like:

\[
(t-s)X \times (-x^3 - 3x^2 + 5x + 14)
\]

However, if you meant for the expression to be separate or involve some other operation, please clarify so I can help you further.

Would you like to explore this expression in more detail, such as multiplying it out or solving for specific values?

---

Here are 5 related questions you might consider:

1. How do you factor complex polynomials like the one simplified above?
2. What happens when you substitute specific values for \(t\), \(s\), and \(X\)?
3. How does the degree of a polynomial affect its graph?
4. What are the roots of the polynomial \(-x^3 - 3x^2 + 5x + 14\)?
5. How can you determine if a polynomial has any symmetry?

**Tip:** Always double-check the distribution of negative signs when subtracting polynomials; it's easy to overlook them!

Explore the algebraic expression (t-s)(X) - (-x^3 - 3x^2 + 5x + 14) with detailed steps and explanations. Learn about algebraic operations, including subtraction of polynomials and multiplication of binomials. Suitable for advanced high school students and college-level algebra enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation