Add and subtract polynomials using algebra tiles

key notes:

1. Introduction to Polynomials:
   • A polynomial is an algebraic expression consisting of variables and coefficients, combined through addition, subtraction, and multiplication.
   • Examples of polynomials include 3�2+2�−53x2+2x−5 and 2�3−�+72y3−y+7.
2. Algebra Tiles:
   • Algebra tiles are physical or visual representations used to model algebraic expressions and equations.
   • They are often square tiles, with different colors representing different variables or constants.
3. Representation of Monomials with Tiles:
   • A monomial is a single term in a polynomial.
   • Use tiles to represent monomials by matching the number of tiles with the coefficient and using variables to represent the power.
4. Addition of Polynomials with Tiles:
   • To add polynomials, arrange the tiles for each polynomial separately and then combine like terms.
   • Like terms are terms with the same variable and exponent.
5. Subtraction of Polynomials with Tiles:
   • To subtract polynomials, arrange the tiles for the minuend and the tiles for the subtrahend, then combine like terms.
6. Zero Pairs:
   • In the process of combining tiles, be aware of zero pairs, where positive and negative tiles cancel each other out.
7. Degree of Polynomials:
   • The degree of a polynomial is the highest power of the variable in any term.
   • When adding or subtracting, make sure to arrange the terms in descending order of degree.
8. Practice Examples:
   • Work through practice problems to reinforce the concept of adding and subtracting polynomials using algebra tiles.
9. Algebraic Notation:
   • Translate the visual representation back into algebraic notation.
   • Understand how tiles correspond to coefficients and variables in the expression.
10. Check Solutions:
    • After performing addition or subtraction using tiles, check the algebraic solution to ensure accuracy.
11. Real-life Applications:
    • Discuss real-life situations where polynomials are used, emphasizing the relevance of these algebraic skills.
12. Problem-solving Strategies:
    • Develop problem-solving strategies, such as breaking down complex expressions into simpler parts and tackling them step by step.

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