Collecting Like Terms. orms. ?. A term in math is a piece of an expression separated by a plus or minus sign. In the expression 3x + 4y – 7 There are three terms. We know what a term is now, so what are like terms?.
In the expression
3x + 4y – 7
There are three terms.
Like terms are terms that have identical variable pieces. In other words, the letters match.
x and x are the same, so they are called like terms. z and z would also be like terms.
Instead of talking about terms let’s talk about worms. “Why worms?” You ask. Because they’re so cute.
Just as before, count up how many of each term you have.
x + x + y + x + y
3 x’s and 2 y’s
We write this as 3x + 2y
Now combine like worms, brown with brown, and yellow with yellow. Since there is only one group of yellow it does not combine with any other worms.
The expression is now:
= 5x + 4y
= 13x + 5y
For example, on the expression 4x + 3y + 2x
we add the like terms to get 6x + 3y.
However, on the expression 4x + 3y – 2x
we subtract the x’s to get 2x +3y.
4x + 7y – 3x – 2y + 3z – 2y
Now collect like terms:
= 2x + 3y
= 3x +2y
When we end up with a negative amount
we can write a minus sign instead of a plus
sign with a negative number.
X2 is like X∙X
These are connected by multiplication and not
addition or subtraction.
This means that X2 is a single term.
Here are some other examples of terms with
X3, Y5, XY, XZ, XYZ, X2Y, X5Y3Z4
= 8x2 + 10xy
Remember x, x2, and x3 are
different terms. You only
combine like terms.
= 2x3 + 12x2 + 7x
By the commutative property we
can rearrange multiplication, so
xy = yx, these are like terms.
= 9xy +3x +4y