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Unit 2.2 Algebraic Expression

Algebraic Expressions

An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. If we look at an algebraic expression like

5x + 4 

“x” is a variable, or an unknown value in the equation. It could be represented by any letter or symbol

5 is a coefficient which is attached to a variable

4 would be considered a constant because its not multiplied by a variable.

These terms are separated by a mathematical operator like multiplication, division, addition and subtraction.

With algebraic expressions, you can combine terms that are of the same value, or “like-terms”

Combining Like Terms, One Variable

If you wanted to combine the two algebraic expressions 5x + 4 and 3x + 2 by addition

Because the variables are the same, we are able to add them

We are NOT able to add the constants with the variables.

So we can combine 5x and 3x and 4 and 2 but not all together

Re-arrange the expression so that the like terms are together. Combining 5x and 3x we get 8x and 4 and 2 we get 6

Because there are no other x values or constants in this equation, we are done simplifying.

Combining Like Terms, 2 Variables

If you wanted to combine the algebraic expressions 8a + 4b and b + 3a + 1 by addition

Locate the values that have the same variable (or are a constant)

We can combine the values with “a” together, the values with “b” together and there is only 1 constant

Rewrite the expression so that the terms that are the same are together and combine the like terms

Because “a” and “b” are different variables, we cannot combine any further

 

Like terms can only be combined if they are the same. It is important to note that x and xare NOT the same value. You cannot combine them together.

Combining Like Terms, x and x2

To combine the expressions x2 + x + 4 and 3x2 + 2x + 1 by addition

Locate the items that are the same value

Re-arrange the expression so the like terms are together

Combine the like terms

Even though there are two “x” in the expression, one of them has an exponent. You cannot combine x2 and x. This is as simplified as it can be.

 

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