We begin with an example
Adam has two rectangles with the same height and he wants to
know the total area of these two rectangles.
He can calculate this in two different ways. Adam can either
calculate the areas separately and then add the two areas.
Or as the height is the same in both rectangles we can multiply
the the height with the sum of the bases
As we can see
This is an example of the distributive property which
can be used to find the product of a number and a sum or a
difference.
The parts of the expression are called terms. A term could
either be a number, a variable, or a product. If we have a term
that contains both a number and a variable as in 2x the number part
of the term, in this case 2, is called the coefficient. A term that
only contains a number and no variable part is called a constant
term.
If we look at the expression:
This expression has 4 terms where two of the terms are constant
terms 5 and -2. The two other terms have the coefficients 3 and 7.
Terms like 3x and 7x that have the same variable part are called
like terms. The constant terms are like terms as well.
Like terms can be combined as is stated in the distributive
property
Expressions like 3x+7x and 10x are equivalent expressions since
they denote the same number.
An expression is written in its simplest form when it contains
no like terms and no parentheses
Example:
Simplify the expression
Notice that the second parenthesis is multiplied by -1. We can
instead write the expression as
By using the distributive property we can rewrite the expression
as
And by combining the like terms we'll get
Which in this case is the simplest form.
Videolesson: Simplify the expression
