Simplifying Expressions A TERM is a number, a variable or the product of a number and one or more variables. A numeric term without a variable is called a constant term or, more simply, a "constant." The numeric part of a term is called the COEFFICIENT. Examples of terms (coefficients in red):
In an algebraic expression, terms are separated by addition. In the expression: 5x + 3x ; 5 and 3 are the coefficients In the expression: 5x - 3x ; 5 and -3 are the coefficients N.B. By definition, terms are separated by addition, so the second expression above should be re-written as: 5x + (-3x) LIKE TERMS are terms where the variable component, including the exponent(s), is the same. Like terms can be COMBINED by simply adding or subtracting the coefficients of the terms. 5x + 3x = 8x <<
add the coefficients >> An expression is said to be in SIMPLEST FORM (i.e. simplified) when it contains NO LIKE TERMS AND NO PARENTHESES. DO NOW - SIMPLIFY: 1) 11x + 4 - 5x + 6 = 2) 7y + (- 7) - (8 + 4y) = 3) 4x2 + 3x - 7 + x - 4x2 =
The Distributive Property ...states that, the product of a and (b+c) is given by a (b+c) = ab + ac
Let's start with the simple stuff: We all agree that 5(6) = 30 N.B. Notice the new and improved
notation!! The SUBSTITUTION PROPERTY allows that any term or expression can be replaced by an equivalent term or expression. Many of us use the substitution property when we do "mental math" with larger numbers. We are actually using the DISTRIBUTIVE PROPERTY!! (aren't we just sooo smart!) 5(63) = 5(60 + 3) = 5(60) + 5(3) = 300 + 15 = 315 In the "lingo" of Algebra, we distributed (or applied) the multiplication by 5 to both the 60 and the 3. Remember, the parentheses make this is a PACKAGE DEAL! The multiplier outside of the package is applied to EVERYTHING inside of the package.
Algebra Tiles can help us VISUALIZE multiplication as the product of the length and width of a rectangle. Web Activity - Algebra Tiles and the Distributive Property
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