"Merge similar items" PPT courseware 2

Description

"Merge similar items" PPT courseware 2

Independent exploration:

1. Observe the following monomials, classify the formulas that you think are of the same type, and state the basis for the classification.

-7ab, 2x, 3, 4ab2, 6ab, 0.6ab2, -3x,-4.5

Classification based on:

Contains the same letters,

exponents with the same letter

Also the same

The concept of similar items:

Terms that contain the same letters and have the same exponent are called homogeneous terms.

Question:

1. What conditions must be met for similar items?

2. Are several constant terms such as -3 and 0.7 also the same kind of terms?

3. Is there any relationship between similar items and the size of the coefficient?

4. Are -3ab and 2ba the same term?

Try it: determine whether the following groups are similar items? (please give reasons)

⑴x and y ⑵a2b and ab2

⑶-3pq and 3qp ⑷abc and ac

⑸a3 and a2 ⑹-0.3 and 2

How to determine similar items:

Contains the same letters,

And the exponents of the same letters are also the same.

3a+2a=(3+2)a=5a

12a2b-3a2b=(12-3)a2b=9a2b

8n+5n=(8+5)n=13n

Question:

1. Among the above three formulas, what is the relationship between 3a and 2a, 12a2b and -3a2b, 8n and 5n?

2. How are they combined into one? What happens to their coefficients, letters, and letter exponents during the merging process?

3. Which kind of operation law we have learned is like this operation?

1. Merge similar items:

The process of merging similar terms in polynomials into one term is called merging similar terms.

2. Rules for merging similar items:

When merging similar terms, the coefficients of similar terms are added, and the letters and letter exponents remain unchanged.

Example 1, merge similar items:

(1) 4ab2-ab-6ab2, (2) 2x2y-5x2y+x2y+5xy2

Solution: (1) 4ab2-ab-6ab2

= (4-6)ab2-ab

=-2ab2-ab

(2) 2x2y-5x2y+x2y+5xy2

=(7+2)a+(3-1)a2+3

=9a+2a2+3

Notice:

1) Merging similar items only adds the coefficients, and the exponents of letters and letters remain unchanged.

2) Items that are not of the same type cannot be merged.

Practice in class:

In each of the following pairs of monomials, there are ( ) similar terms

(1) x and y (2) a2b and ab2

(3)-3pq and 3qp (4) bc and ac

(5) a2 and a3

(A) 1 piece (B) 2 pieces (C) 3 pieces (D) 4 pieces

I use my knowledge

At what value of K will 3xky and -x²y be the same kind of terms?

summary

What are similar terms?

What is merging similar items?

How to merge similar items?

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Update Time: 2024-07-04

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