Learn to identify and combine like terms to simplify expressions.
Preview · progress not saved — Chapter 1 is free
Introduce simplification via rectangle perimeter.
When we find the perimeter of a rectangle, we add the lengths of all four of its sides. If we use the letter-numbers for length and for breadth, the perimeter can be written as:
Visualizing area models or grouping physical objects helps explain like terms.
Adding the areas of two smaller rectangles visualizes how like terms such as 4v and 3v combine to make 7v.
Define like and unlike terms explicitly.
Like terms are sets of terms that involve the exact same letter-numbers (variables). For example, the terms , , and are like terms because they all share the variable .
Similarly, and are like terms.
Example 5 from page 88.
A shopkeeper sells pencils and erasers over three days. The price per pencil is , and the price per eraser is .
Find the total money earned by the shopkeeper during these three days.
Faded example for Example 7.
To find the total cost of renting the furniture, we subtract the amount returned from the amount paid upfront: .
Opening the brackets gives us the full expression: .
Next, we swap the terms so that like terms are next to each other, and group them as .
By calculating the numbers inside the brackets, we arrive at the final simplified expression for the total cost: + 65y.
Spot the simplification error.
Simplify the expression:
Practice combining terms with multiple variables.
Work through the steps to simplify the algebraic expression
Write out the starting algebraic expression.
What mathematical rule allows you to combine these terms?
Rearrange the expression so that the terms with 'p' are together and the terms with 'q' are together.
Show the subtraction happening between the numbers (coefficients).
State your final, fully simplified answer.
Briefly explain why you stopped here.