Algebraic Expressions

First, we’ll talk about some algebraic expressions before we are going over a few examples and talk about a few of our algebraic terms here.

So first, what do we mean by an algebraic expression? Well, I guess you do remember what we mean by a numerical expression. We’ve been talking about that earlier.


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1. Simplify this algebraic expression:
\(5(a + 7) + 2(a + 4)\)

Question 1 of 2

2. Simplify: \( 3(b + 4) + 5(b + 2)\)

Question 2 of 2


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Video Transcription

Numeric expressions include numbers & operations. Basically, that’s it. They don’t have equal signs. Remember this: expressions don’t have equal signs. Those are equations. Algebraic Expressions differ from Numerical Expressions because they include variables.

Algebraic expressions are those expressions that contain numbers, operations, and one or more variables. So, in this case, we have a variable. We have an operation, and we have numbers. We can’t see our operation; however, if 3x or xy are placed next to each other, that is meaning multiplication.

So we have an operation. So these are all examples of our algebraic expressions.

But when we have something like that, it is not an algebraic expression as we have no variable. So that would be just one numerical expression.
The same thing, when we have: 3 x + 4 = 10

This is also not an algebraic expression, though it has some variable operations. There is an equal sign, and that means it is an equation and not an expression at all.

So make sure that you understand what algebraic expressions are.
Make also sure to understand what they include.

So again, when we talk about Algebraic Expression, we talk about expressions that contain numbers, operations, and 1 or more variables. This makes them different from numerical expressions.

In Numeric Expressions, there are no equal signs; they just include numbers and operations. So expressions don’t have equal signs. If there are equal signs, they are equations. Well, Algebraic Expressions differ from numerical expressions since they contain variables.

Again, Algebraic Expressions contain operations, numbers, and 1 or more variables. If you have a variable, an operation, and numbers, we deal with an Algebraic Expression.