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Collecting Like Terms

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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?

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.

3

2

x

y

x

y

x

x

y

x

x

y

x

y

x

3

x

y

2

Let’s look at this as an expression.

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

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

The expression is now:

7

3

- 3x + 4y + 2x
- 7x + 2y + 6x + 3y
- 12z + 14z + 13z

= 5x + 4y

= 13x + 5y

= 39z

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:

x

+ 3y

+ 3z

= 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.

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

- 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

- 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