Add and subtract polynomials using algebra tiles

Learning Objectives Identify and represent positive and negative constant and variable terms using algebra tiles. Model any given polynomial expression using algebra tiles. Explain and apply the concept of 'zero pairs' when simplifying expressions with algebra tiles. Accurately add two or more polynomials by combining like terms using algebra tiles. Accurately subtract one polynomial from another by applying the 'add the opposite' strategy with algebra tiles. Simplify polynomial expressions after addition or subtraction, translating the final tile representation back into an algebraic expression. Ever wonder how to combine different types of items, like apples and oranges, but with numbers and letters? 🍎🍊 Let's discover a fun, hands-on way to do ju...

TermDefinitionExample Algebra TilesPhysical or virtual manipulatives used to represent numbers, variables, and algebraic expressions. They come in different shapes and colors to distinguish between constants, variables (like 'x'), and their positive/negative values.A small yellow square represents +1, a small red square represents -1. A long green rectangle represents +x, a long red rectangle represents -x. PolynomialAn algebraic expression consisting of one or more terms, where each term is a product of a number (coefficient) and one or more variables raised to non-negative integer powers.$$3x + 2$$ is a polynomial. $$x^2 - 5x + 7$$ is also a polynomial. TermA single number, a single variable, or a product of numbers and variables within an algebraic expression. Terms are separ...

Representing Positive and Negative Terms Positive terms are represented by one color (e.g., yellow for +1, green for +x). Negative terms are represented by an opposite color (e.g., red for -1, red for -x). This rule establishes the visual convention for algebra tiles, allowing you to distinguish between positive and negative values in an expression. For example, to represent $$3x - 2$$, you would use three green 'x' tiles and two red unit tiles. The Zero Pair Rule Any positive tile combined with its corresponding negative tile creates a 'zero pair' and can be removed from the model without changing the value of the expression. $$(+1) + (-1) = 0$$ and $$(+x) + (-x) = 0$$ This rule is fundamental for simplifying expressions. When you have an equal number of...