"Merge similar items" PPT courseware 4

Description

"Merge similar items" PPT courseware 4

Mathematics exists everywhere in life. Things with the same characteristics can be grouped into one category. In polynomials, terms with the same characteristics can also be grouped into one category and then combined.

Question 1: What are the terms in the above polynomial?

3x2, -4xy², -3, 5x2, 2xy², 5

Question 2: Which terms in the above polynomial do you think can be classified into the same category?

3x2 and 5x2

-4xy2 and 2xy2

-3 and 5

What characteristics do items classified into the same category have in common?

Definition: In polynomials, terms that contain the same letters and have the same exponent with the same letters are called similar terms.

All constant terms are also treated as similar terms.

Discriminate: Are the two items in each of the following groups the same type? Why?

(1)2a and 2ab; (2)2a2b and 2ab2;

The letters contained are the same; the exponents of the same letters are also the same.

(3)3xy and -1/2yx; (4) -2.1 and 3/4.

Alphabetical order has nothing to do with it; coefficients have nothing to do with it.

Note: all constant terms are also treated as similar terms.

Kind tips

Two conditions (two are the same) are indispensable;

Similar terms have nothing to do with coefficients or the order of letters; for example - 2xy, 5xy and yx

All constant terms are of the same type, such as 1 and -3.

Small test

In each of the following pairs of monomials, similar terms have _________

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

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

(5) a2 and a3

Example 1, merge similar items:

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

(2)-4ab+8-2b²-9ab-8

step:

(1) Find similar items (draw them with lines);

(2) Determine the coefficients of each similar item;

(3) Merge similar items;

(4) Individual items are written at the back. (It does not mean that similar items cannot be merged.)

The game just now

Find the value of the algebraic expression -4x2+7 x+3 x2-4 x+ x2. Give X a positive integer value less than 100 and compare to see who can get the answer the fastest.

I expand my thinking

(1) If the algebraic expression about the letter x -3x2 +ax+bx2 +2 x+3 does not contain the linear term of x after being combined, then the following statement is correct (　)

A. a+b=0 B. a=0

C. b=3 D. a=-2

(2) It is known that the difference between the monomial 2x6y2m+1 and -3x3ny5 is still a monomial, then the value of mn is ____

independent work

1. There is such a question:

When a=0.35, b=-0.28, find the value of the polynomial:

a3b+2a3－2a2b+3a3b+2a2b－2a3－4a3b

One student pointed out: The conditions a=0.35 and b=-0.28 given in the question are redundant.

Does his statement make sense?

2. Complete the workbook

There is such a question:

When a=0.35, b=-0.28, find the value of the polynomial:

a3b+2a3－2a2b+3a3b+2a2b－2a3－4a3b

One student pointed out: The conditions a=0.35 and b=-0.28 given in the question are redundant.

Does his statement make sense?

Solution: After simplification, the original polynomial is zero. Therefore, no matter what the values ​​of the letters a and b in the formula are, the value of the polynomial is 0.

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"Merge similar items" PPT courseware 3:

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"Merge similar items" PPT courseware 2:

"Combining Similar Terms" 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 classification -7ab, 2x, 3, 4ab2, 6ab, 0.6ab2, -3x -4.5 Classification basis: Containing the same letters, similar...

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Update Time: 2024-09-08

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