https://file.aiquickdraw.com/mathbot/file/172757041607037wm2ztl.jpg

https://file.aiquickdraw.com/mathbot/file/17275704160704tfg71hr.jpg

CHO CÔNG THỨC, LÝ THUYẾT, LƯU Ý, TRƯỜNG HỢP:

The two images you uploaded contain various algebraic polynomial problems, including sums, differences, and factorizations of polynomials, as well as operations like multiplying polynomials by monomials.

Let me summarize the different types of questions and topics covered in both images:

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### Image 1: Polynomial Addition, Subtraction, and Finding Unknown Polynomials

**Part 1**: Basic Operations with Polynomials
1. **Addition and Subtraction** of Polynomials
   - Example: \( P(x) + Q(x) \) and \( P(x) - Q(x) \)
2. In some problems, there are three polynomials involved: \( P(x), Q(x), R(x) \).
   - Example: \( P(x) - Q(x) - R(x) \)

**Part 2**: Finding Unknown Polynomials
1. Given equations like \( A(x) - B(x) = x^2 - 1 \), find the unknown polynomials \( B(x) \) and \( C(x) \).
   - Example: \( A(x) - C(x) = x^3 + 2x - 6 \)

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### Image 2: Polynomial Multiplication and Simplification

**Part 1**: Multiplying Monomials and Polynomials
1. **Multiplying Monomials** with Polynomials:
   - Example: \( x(2x^2 - x + 1) \)
   - Another example involves multiplying a cubic monomial by a trinomial.

**Part 2**: Simplifying Expressions and Substituting Values
1. **Simplify and Substitute Values** into expressions:
   - Example: \( D(x) = (x^2 - y^2) + (x^2 y - xy + x^2) \) at \( x = \frac{1}{2}, y = -2 \)
   - Another similar example for a different polynomial \( E(x, y) \)

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Would you like me to solve specific problems from the images or provide theory and explanations on specific operations such as addition, subtraction, multiplication of polynomials, or substitution? Feel free to ask about particular problems or steps you need help with!

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### Relative Questions:
1. How do you simplify the subtraction of two polynomials like \( P(x) - Q(x) \)?
2. What is the method to find an unknown polynomial from an equation like \( A(x) - B(x) = x^2 - 1 \)?
3. How can you approach multiplying a monomial by a polynomial?
4. What steps are involved in simplifying and evaluating polynomial expressions with given values?
5. What rules govern the addition and subtraction of higher-degree polynomials like cubic and quartic polynomials?

### Tip:
Always arrange polynomials in descending order of degree and align like terms when adding or subtracting to avoid mistakes.

CHO CÔNG THỨC, LÝ THUYẾT, LƯU Ý, TRƯỜNG HỢP

This page provides a collection of algebraic problems focused on polynomial addition, subtraction, and multiplication, along with simplification and substitution of polynomial expressions. These problems are suitable for students in Grades 7-9.

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