Download Collecting Like Terms

Collecting Like
Terms
o
?
A term in math is a piece of an
equation separated by a plus or
minus sign.
In the equation
3x + 4y – 7
There are three terms.
We know what a term is now, so
what are like terms?
Like terms are terms that have
identical variable pieces. In other
words, the letters match.
x, y, and z are all different variables.
So each of these is a different term.
x and x are the same, so they are
called like terms. z and z would
also be like terms.
Let’s forget about math for a few
minutes.
Instead of talking about terms let’s talk about
worms. “Why worms?” You ask. Because
they’re so cute.
See. Okay, okay. How about now?
We have a box of worms.
Some are brown and some are green.
We have two types of worms. Let’s
collect the worms into groups by color.
How many of each color do we have?
3
2
Back to math. Instead of worms, now
we have terms. Instead of grouping by
colors we group by the same variables.
(like terms)
x
y
x
y
x
Just imagine the letters are worms
and collect them like before.
x
x
y
y
x
Now count up how many of each
we have.
3x
x
2y
y
x
Let’s look at this as an equation.
x+x+y+x+y
Just as before, count up how
many of each term you have.
3 x’s and 2 y’s
We write this as 3x + 2y
But worms are social creatures. Well,
not really, but what if they’re traveling
in groups instead of individually?
In this case we take the number in
each group and combine them.
4
3
3
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.
4
7
3
3
Let’s look at some examples using
equations.
• 3x + 4y + 2x = 5x +4y
• 7x + 2y + 6x + 3y = 13x + 5y
• 12z + 14z + 13z
= 39z
Collecting like terms(worms) can also
be used when reducing a group. We
can subtract or add negative amounts.
For example, on the equation 4x + 3y + 2x
we add the like terms to get 6x + 3y.
However, on the equation 4x + 3y – 2x
we subtract the x’s to get 2x +3y.
The trick to subtraction is to
remember that each number goes
with the sign or operation that comes
before it.
4x + 7y – 3x – 2y + 3z – 2y
Now collect like terms:
x + 3y + 3z
Try these.
• 4x + 3y -2x = 2x + 3y
• 7x – 6y – 4x + 8y = 3x + 2y
• 7z + 8x – 3z – 10x = 4z – 2x
When we end up with a negative amount
we can write a minus sign instead of a plus
sign with a negative number.
What about exponents?
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
multiple variables:
X3, Y5, XY, XZ, XYZ, X2Y, X5Y3Z4
Try these examples.
• 3x2 + 7xy + 5x2 + 3xy
= 8x2 + 10xy
• 4x2 + 5x + 2x3 + 8x2 + 2x
= 2x3 + 12x2 + 7x
• 5xy + 3x + 4yx + 4y
= 9xy +3x +4y
Remember x, x2, and x3 are
different terms. You only
combine like terms.
By the commutative property we
can rearrange multiplication, so
xy = yx, these are like terms.
Still having trouble?
• Try color coding, use colored pencils to
identify the like terms.
3x +
4y
+ 2xy + 6x + 4xy
• Or use pictures for the situation (like worms).
3x +
4y
+ 2xy + 6x + 4xy