Skip to main content
Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

Simplifying Expressions

Algebraic expressions can sometimes look messy since they contain alphabetic symbols are well as numbers. Let's take a closer look at how we can simplify these expressions. 

To simplify an algebraic expression, we must gather like terms. When an algebraic expression is simplified, an equivalent expression is found that is simpler than the original. This usually means that the simplified expression is smaller than the original expression. There are many different kinds of algebraic expressions, so there is no standard procedure for simplifying all of them. Here is a list of steps to follow.

  • Prepare the algebraic expression to be simplified (such as through expanding).
  • Identify and group like terms.
  • Combine like terms.

Example: Simplify the expression 5x + 3y -9z -8x + 6y.

Solution:

The expression does not need to be prepared, so first identify and group like terms:

(5x - 8x) + (3y + 6y) - 9z

Next, combine like terms:

-3x + 9y - 9z

Example: Simplify the expression 4(5a - 4b) -7(6a + 2b).

Solution:

First, prepare the expression to be simplified (expand): 20a - 16b - 42a- 14b

Next, identify and group like terms: (20a - 42a) + (-16b - 14b)

Lastly, combine like terms: -22a - 20b

It is important to understand that not all algebraic expressions can be simplified. For example, the expression 56a - 8b + 7c -5 cannot be simplified any further since there are no like terms in the expression.

Let's finish off with one more example of an expression that has products and quotients of simple factors that include powers with the same base. They can be easily simplified by adding and subtracting the indices of the powers (using exponent laws).

Example: Simplify the expression 24w4x5z ÷ 2wyz2

Solution:

The expression does not need to be prepared, so combine like terms: 12w3x5/yz

Example - Combining Rational Expressions:

Avoiding Common Math Mistakes when Simplifying: