Subtraction with pictures

Learning Objectives Model the subtraction of polynomials using algebra tiles. Represent the subtraction of variable expressions as finding the difference in areas of geometric shapes. Translate a visual representation of subtraction (like algebra tiles or area models) into a symbolic algebraic expression. Solve linear equations involving the subtraction of expressions by visualizing the distribution of the negative sign. Simplify polynomial expressions involving subtraction by visually grouping like terms. Justify the rule for subtracting polynomials by connecting it to the 'add the opposite' concept shown with pictures. Ever designed a custom phone background and needed to cut out a space for your widgets? 📱 How do you calculate the remaining area when the dimens...

TermDefinitionExample PolynomialAn expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.3x² + 2x - 5 is a polynomial. Like TermsTerms whose variables (and their exponents) are the same. In pictures, these are represented by tiles of the same shape and size.In the expression 4x² + 3x - 2x², the terms 4x² and -2x² are like terms. Algebra TilesA set of manipulatives used to represent algebraic concepts. A large square represents x², a rectangle represents x, and a small square represents the constant 1. Shaded tiles represent positive values and unshaded/red tiles represent negative values.The expression 2x² - x + 3 can be shown with two large positive squares, one...

Subtraction as Adding the Opposite A - B = A + (-B) To subtract an expression (B), you can add its opposite (-B). Visually, this means instead of 'taking away' tiles, you can 'add' the negative version of those tiles. Distributive Property for Subtraction A - (B + C) = A - B - C \quad \text{and} \quad A - (B - C) = A - B + C When subtracting an entire expression in parentheses, the negative sign must be distributed to EVERY term inside the parentheses. This is like flipping the sign of every tile you are subtracting.