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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?.

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A term in math is a piece of an expression separated by a plus or minus sign

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

We know what a term is now, so what are like terms? plus or minus sign.

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 plus or minus sign., 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

Let’s forget about math for a few minutes. plus or minus sign.

Instead of talking about terms let’s talk about worms. “Why worms?” You ask. Because they’re so cute.


See. plus or minus sign.


We have a box of worms some are brown and some are green
We have a box of worms. plus or minus sign.Some are brown and some are green.


W e have two types of worms let s collect the worms into groups by color
W plus or minus sign.e have two types of worms. Let’s collect the worms into groups by color.


How many of each color do we have
How many of each color do we have? plus or minus sign.

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




Let s look at this as an expression

Let’s look at this as an expression. before.

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


But worms are social creatures. Well, not really, but before.what if they’re traveling in groups instead of individually?



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

The expression is now:

7

3


Let s look at some examples
Let’s look at some examples. yellow. Since there is only one group of yellow it does not combine with any other worms.

  • 3x + 4y + 2x

  • 7x + 2y + 6x + 3y

  • 12z + 14z + 13z

= 5x + 4y

= 13x + 5y

= 39z


Collecting like terms(worms) can also be used when reducing a group. We can subtract or add negative amounts.

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.


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
Try these. goes with the sign or operation that comes before it.

= 2x + 3y

  • 4x + 3y -2x

  • 7x – 6y – 4x + 8y

  • 7z + 8x – 3z – 10x

= 3x +2y

=-2x +4z

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
What about exponents? goes with the sign or operation that comes before it.

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
Try these examples. goes with the sign or operation that comes before it.

  • 3x2 + 7xy + 5x2 + 3xy

  • 4x2 + 5x + 2x3 + 8x2 + 2x

  • 5xy + 3x + 4yx + 4y

= 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


Still having trouble
Still having trouble? goes with the sign or operation that comes before it.

  • Try color coding, use colored pencils to identify the like terms.

  • Or use pictures for the situation (like worms).

+

4xy

+

6x

+

2xy

4y

3x

+

+

+

+

6x

2xy

4y

3x

+

4xy


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