# Collecting Like Terms - PowerPoint PPT Presentation

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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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Collecting Like Terms

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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.

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

### 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

The expression is now:

7

3

### Let’s look at some examples.

• 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.

= 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

sign with a negative number.

X2 is like X∙X

These are connected by multiplication and not

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

• 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?

• 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