Learn to simplify algebraic expressions A term can

Learn to simplify algebraic expressions.

A term can be a number, a variable, or a product of numbers and variables. 7 x term + 5 – term 3 y 2 + term One Term y+ x 3 term

Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, 1, 2 and 3. 2, are also like terms. Like Terms Unlike Terms w and w 5 and 1. 8 7 5 x 2 and 2 x 6 a and 6 b 3. 2 and n The exponents The variables Only one term contains a are different variable 3 x and 2 x

Additional Example 1: Identifying Like Terms Identify like terms in the list. 3 t 5 w 2 7 t 9 v 4 w 2 8 v Look for like variables with like powers. 3 t 5 w 2 7 t 9 v Like terms: 3 t and 7 t 4 w 2 8 v 5 w 2 and 4 w 2 9 v and 8 v Helpful Hint Use different shapes or colors to indicate sets of like terms.

Combining like terms is like grouping similar objects. x x 4 x + + x x 5 x x = = x x x x x 9 x To combine like terms that have variables, add or subtract the coefficients.

Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3 a 2 + 5 b + 11 b 2 – 4 b + 2 a 2 – 6 (3 a 2 + 2 a 2) + (5 b – 4 b) + 11 b 2 – 6 5 a 2 + b + 11 b 2 – 6 Identify like terms. Group like terms. Add or subtract the coefficients.

Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5 y + 3 y 8 y 5 y and 3 y are like terms. Add the coefficients. B. 2(x 2 – 13 x) + 6 2 x 2 – 26 x + 6 Distributive Property. There are no like terms to combine.

Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4 x 2 + 4 y + 3 x 2 – 4 y + 2 x 2 + 5 Identify like terms. (4 x 2 + 3 x 2 + 2 x 2)+ (4 y – 4 y) + 5 Group like terms. 9 x 2 + 5 Add or subtract the coefficients.

Additional Example 3: Geometry Application Write an expression for the perimeter of the triangle. Then simplify the expression. 2 x + 3 3 x + 2 x Write an expression using the side lengths. (x + 3 x + 2 x) + (2 + 3) Identify and group like terms. 6 x + 5 Add the coefficients. 2 x + 3 x + 2 + x