Bell Quiz

Objectives Learn to identify and combine like terms within an algebraic expression.

Combining like Terms Two or more terms that have the same variable or variables raised to the same power are like terms. Terms with different variables or terms with the same variable or variables raised to a different power are unlike terms.

Combining like Terms 3x 4 + 5y 4 + 5x 4 Because the variable x has the same power, 3x 4 and 5x 4 are like terms. Because the variables are not the same, 5y 4 and 5x 4 are unlike terms. The coefficient is not used to establish whether the terms are like or unlike ○ ○

Example 1 Combining like Terms without Exponents Simplify each expression 5x + 7x

Example 2 Combining like Terms without Exponents Simplify each expression – 4y – (– 3y) + 5y

Example 3 Combining like Terms without Exponents Simplify each expression 6xy – 3a + 4xy

Lesson Practice Simplify each expression – 2xy – 3x + 4 – 4xy – 2x

Lesson Practice Simplify each expression 7m – (– 8m) + 9m

Lesson Practice Simplify each expression 3yac – 2ac + 6acy

Example 4 Combining like Terms with Exponents Simplify each expression x 5 + y 3 + x 5 + y 3

Example 5 Combining like Terms with Exponents Simplify each expression 3k 2 – 2k 2 + 4k 2 + 2kx 4 + kx 4

Example 6 Combining like Terms with Exponents Simplify each expression 2x 2 y 3 + xy – 8y 3 x 2 – 5yx

Lesson Practice Simplify each expression x 4 y + 3x 4 y + 2x 4 y

Lesson Practice Simplify each expression x 2 y – 3yx + 2yx 2 – 2xy + yx

Lesson Practice Simplify each expression m 3 n + m 3 n – x 2 y 7 + x 2 y 7

Example 7 Application: Measurement Olympic competition offers three equestrian disciplines: dressage, show jumping, and endurance. The diagram represents the measurements for a regulation dressage arena. Find the perimeter of the arena as a simplified variable expression. Then evaluate the expression for x = 19.5 meters. 3x + 3 x – 1

Lesson Practice A triangular-shaped display case has the dimensions shown on the diagram. Find the perimeter of the display case as a simplified algebraic expression. Then evaluate the expression for x = 2 feet x + 1 x2x2 x 2 +1