https://file.aiquickdraw.com/mathbot/file/17263649498927ta8qqcl.jpg

a) Tính A(x) + B(x)
b) Tính A(x) – B(x)


Let's analyze the image to extract the mathematical expressions for \( A(x) \) and \( B(x) \).

From the image, we can see the following functions:

\[
A(x) = 5x^4 + x^3 + \frac{1}{2}x^2 + 2x + 2
\]
\[
B(x) = 5x^4 - x^3 + \frac{1}{2}x^2 - 10x - 3
\]

### a) Tính \( A(x) + B(x) \)

\[
A(x) + B(x) = (5x^4 + x^3 + \frac{1}{2}x^2 + 2x + 2) + (5x^4 - x^3 + \frac{1}{2}x^2 - 10x - 3)
\]

Let's combine like terms:

\[
A(x) + B(x) = (5x^4 + 5x^4) + (x^3 - x^3) + \left(\frac{1}{2}x^2 + \frac{1}{2}x^2\right) + (2x - 10x) + (2 - 3)
\]

Simplifying:

\[
A(x) + B(x) = 10x^4 + 0x^3 + x^2 - 8x - 1
\]

So:

\[
A(x) + B(x) = 10x^4 + x^2 - 8x - 1
\]

### b) Tính \( A(x) - B(x) \)

\[
A(x) - B(x) = (5x^4 + x^3 + \frac{1}{2}x^2 + 2x + 2) - (5x^4 - x^3 + \frac{1}{2}x^2 - 10x - 3)
\]

Now distribute the negative sign:

\[
A(x) - B(x) = 5x^4 + x^3 + \frac{1}{2}x^2 + 2x + 2 - 5x^4 + x^3 - \frac{1}{2}x^2 + 10x + 3
\]

Combine like terms:

\[
A(x) - B(x) = (5x^4 - 5x^4) + (x^3 + x^3) + \left(\frac{1}{2}x^2 - \frac{1}{2}x^2\right) + (2x + 10x) + (2 + 3)
\]

Simplifying:

\[
A(x) - B(x) = 0x^4 + 2x^3 + 0x^2 + 12x + 5
\]

So:

\[
A(x) - B(x) = 2x^3 + 12x + 5
\]

### Final Answers:
- \( A(x) + B(x) = 10x^4 + x^2 - 8x - 1 \)
- \( A(x) - B(x) = 2x^3 + 12x + 5 \)

Would you like further details or explanations?

Here are 5 related questions for practice:
1. What is \( A(x) \times B(x) \)?
2. How would you calculate \( \frac{A(x)}{B(x)} \)?
3. Can you find the roots of \( A(x) - B(x) = 0 \)?
4. What is the degree of the polynomial \( A(x) + B(x) \)?
5. How would the solution change if \( A(x) \) or \( B(x) \) included a term with \( x^5 \)?

**Tip:** When simplifying polynomials, always group like terms first to avoid mistakes with signs or coefficients.

a) Tính A(x) + B(x)
b) Tính A(x) - B(x)

Learn how to compute the sum and difference of two polynomials, A(x) and B(x), with detailed steps for combining like terms and simplifying expressions. This problem covers key algebraic concepts suitable for Grades 9-11 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation