Bell Work:

Use the distributive property to evaluate

4(6 – 2 + 5 – 7)

Answer:

4(6 – 2 + 5 – 7)

= 24 – 8 + 20 – 28

= 16 + 20 – 28

= 36 – 28

= 8

Lesson 18: Like Terms, Addition of Like Terms

Like terms are terms that have the same variables in the same form or in equivalent forms so that the terms represent the same number regardless of the nonzero values assigned to the variables.

Example:

In the expression

4xmp – 2pmx + 6mxp

Are xmp, pmx, and mxp like terms?

Answer: 4xmp – 2pmx + 6mxp

Let x = 4, m = 2, and p = 6.

Don’t worry about the leading coefficients right now.

(4)(2)(6) = 48 (6)(2)(4) = 48 (2)(4)(6) = 48

They are like terms

2 statements regarding like terms

1. They are in equivalent forms, for they have the same variables in the form of an indicated product, and the order of multiplication of the factors does not affect the value of the product.

2. They represent the same number regardless of the nonzero values assigned to the variables.

Addition of like terms:

The extension of the distributive property can be rewritten as

ba + ca + da + … = (b + c + d + …)a

We note that “a” is a common factor of each of the terms on the left and is written outside the parentheses on the right.

If we look at the indicated sum of terms

4xmp – 2pmx + 6mxp

We see that the factor xmp is a factor of all three terms and can be treated in the same manner as the “a” factor before.

Thus, we can rewrite

4xmp – 2pmx + 6mxp

As

(4 – 2 + 6)xmp = 8xmp

The factors of the three variables in the expression 8xmp could be written in any order without changing the value of the expression.

To add like terms, we algebraically add the numerical coefficients.

Practice:

Simplify by adding like terms:

3x + 5 – xy + 2yx – 5x

Answer:

3x + 5 – xy + 2yx – 5x

= -2x + xy + 5

Practice:

Simplify by adding like terms:

3xy + 2xyz – 10yx – 5yzx

Answer:

3xy + 2xyz – 10yx – 5yzx

= -7yx – 3xyz

Practice:

Simplify by adding like terms:

4 + 7mxy + 5 + 3yxm - 15

Answer:

4 + 7mxy + 5 + 3yxm – 15

= -4 + 10mxy

Practice:

Simplify by adding like terms:

3x – x – y + 5 – 2y – 3x – 10 – 8y

Answer:

3x – x – y + 5 – 2y – 3x – 10 – 8y

= -x – 11y – 5

Practice:

Simplify by adding like terms:

-3 + xmy – y – 5 + 8ymx – 3y – 14

Answer:

-3 + xmy – y – 5 + 8ymx – 3y – 14

= -22 – 4y + 9myx

HW: Lesson 18 # 1-30

Due Tomorrow