How to merge similar items, how to merge similar items

Merging similar terms is using the multiplicative distributive property. Merging similar terms is actually the inverse application of the multiplicative distributive law. That is, each term of the same kind is regarded as the product of two factors, and since each term contains the same letter and their exponents are the same, each term of the same kind contains the same factor.

The distributive law is reversed when merging, multiplying the same factor by the algebraic sum of the other factor in the terms.

For example, a, 3a, and 7a are the same category.

In polynomial 3a, 4ab, 5a, 7+15ab, +29, 3a and 5a are the same term.

4ab is the same as 15ab.

7 and 29 are also the same category.

The law of merging similar terms.

1) After merging the same kind of items, the coefficient of the obtained item is the sum of the coefficients of the same kind of items before the merger, and the letter together with its index remains unchanged. The letters do not change, and the coefficients are added and subtracted.

b) The coefficients of the same kind are added together, and the result obtained is used as a coefficient, and the letters and the exponents of the letters are unchanged.

Example: 5x+2x

5+2)x add two numbers with different signs, take the sign of the addition with the greater absolute value, and subtract the absolute value of the smaller number from the absolute value of the larger number. -3x example:

2（2x-3y）

4x+6y=-2 2x+(-3)y(-2) multiply the same sign, and the result is positive; Multiply the different signs and the result is negative.

Example: (-a)=a

a|=aa|=a

The coefficients are added to the coefficients of the result, and the letters and the exponents of the letters remain unchanged. Symbols and walk ahead.

Example: 5xy+3x+2xy

5xy+2xy)+3x

3xy+3x

It is recommended that you use linked lists for polynomials...

1. Merge similar terms: Merge similar terms in a polynomial into one term, which is called merging similar terms. The rule of merging terms of the same kind is: the coefficients of the same terms are added, and the result is taken as a coefficient, and the letters and the exponents of the letters are unchanged.

2. The rule of removing brackets: the "+" sign in front of the parentheses, remove the brackets and the "+" sign in front of it, and the items in the brackets are unchanged symbols; The parentheses are preceded by the "—" sign, remove the brackets and the "—" sign in front of it, and change the symbols of each item in the parentheses.

3. The rule of adding brackets: after adding the brackets, the brackets are preceded by the "+" sign, and the items in the brackets are unchanged symbols; After adding parentheses, the parentheses are preceded by a "—" sign, and the symbols of each item in the parentheses are changed.

For example, find the maximum value of the algebraic formula -2m squared - 6m+12 and the minimum value of 2x square + 4x+8.

Solution: -2m -6m + 12 = -2 (m + 3m + 9 4) + 12 + 9 2 = -2 (m + 3 2) +33 2, the maximum value is 33 2.

2x +4x+8=2(x +2x+1)+6=2(x+1) +6, the minimum value is 6.

Merging similar terms is to use the multiplicative distributive law, the coefficients of similar terms are added, and the result is used as coefficients, and the letters and exponents are unchanged.

For example, merge the same kind of items 8ab+6ab 3ab

Analysis: When the same kind of terms are combined, the coefficients of the same kind are added or subtracted, and the letters and the exponents of each letter do not change.

Answer: Original formula = ( 8 + 6 3) ab = 5 ab.

The way to merge items of the same kind is:

The coefficients of the same kind are added together as the combined coefficients, and the letters and the exponents of the letters remain unchanged.

Merge items of the same kindThe method of merging the dough with the same kind of terms requires the exchange of the number of positions, paying attention to the symbolic nature of each coefficient, not just the exchangeAbsolute, and lose the symbol, and then all merge into the same term, you need to use the additive associative law andMultiplication divides the and the rhythmIf the coefficient of the first item in the parentheses is negative, it is recommended to restore the "+" sign in front of this item, and first observe whether there is a representation of the number of Mori TangerineOpposite numbercan be directly cancelled out, and finally a simple formula such as (a-b) can sometimes be seen as a whole, i.e., as a letter.

Merging similar terms is to put polynomials.

After merging, the coefficient of the obtained item is the sum of the coefficients of the similar items before the merger, and the letter part remains unchanged, the law of merging the same items: the coefficients of the same kind are added, and the result is used as a coefficient, and the exponent of the letter and the letter is unchanged.

Merging similar terms is to use the multiplicative distributive law, the coefficients of the same kind are added, and the result is as the coefficient, the letters and exponents are unchanged, the merging of similar terms is actually the reverse application of the multiplicative distributive law, that is, each term of the same kind is regarded as the product of the coefficient and another factor, because each item contains the same letter and their exponents are also the same, so each term of the same kind is the product of the coefficient and the same other factor, and the distributive law is used in reverse when merging, Multiply the same factor by the algebraic sum of the coefficients.

(1) In the merger of similar terms, it is necessary to exchange the position of the additive, pay attention to the symbolic nature of each coefficient, and not only exchange the absolute value, but lose the symbol.

2) In the total merger of similar terms, it is necessary to use the inverse operation of the additive associative law and the multiplicative distributive law, and when adding parentheses, if the coefficient of the first term in the parentheses is negative, it is recommended to restore the "+" sign in front of this term.

3) Observe whether there are terms that represent opposite numbers, which can be directly offset.

4) Sometimes a simple formula such as (a-b) can be seen as a whole, i.e., as a single letter.

Easy calculation:

Simple arithmetic to make up integers, first exchange and then combine; A number is subtracted by a number in a row, which is equal to the sum of the next number minus the next number; A number is divided by several numbers consecutively, which is equal to the number divided by the next few products.

Several numbers and multiply a number, multiply and add respectively, multiply the difference by a number, multiply and subtract respectively, the same number is proposed, and the rest is enclosed in parentheses. Add more to subtract, add more to subtract, add less to add, and subtract less to subtract.

It seems to be a way to solve the common algebraic solutions in middle and high school mathematics, and I have forgotten what the specific "merging similar terms" rule is, but the example is very simple: (e.g.) ax +by +cn +4x +5y +6n = (a, b, c are constants, that is, pure numbers) merging is a bit like calculating equations to get (a+4)x

b+5）y²

c+6）n²=α

"Like-of-kind" is actually the "same letter" term, that is, the "unknown" term, and "merging the same kind" is to merge the same unknown (which can be simply understood as the same unknown factor) items together. The coefficients, enclosed in parentheses, and multiplied by what they have in common is "merging similar terms".

It's kind of like elementary school math.

Simple algorithm: multiplication combined.

For specific rules, please refer to the rules in high school math books.

Because the old man has said goodbye to his student days for many years, there may be some lack of language, please bear with me!

Merging similar terms in a polynomial into one is called merging similar terms.

Note (1) When merging similar items, pay attention to the merging only coefficients, and the letter parts remain unchanged, so do not omit them;

2) When merging similar terms, pay attention to the symbols of each coefficient, especially when the coefficient is negative, do not omit the negative sign, and do not lose the item;

3) If the coefficients of two terms of the same kind are inverse to each other, the result of merging the terms of the same kind is 0.

You can refer to the above steps.

Ask how to determine the symbols.

The ones at the bottom, are you tired of copying, I'm tired of reading it, can't I write it myself?

Merge the same kind of item symbol as follows:

For example: 2a+3b+a+(-5)b

2a+a+3b+(-5)b

3a+(-5+3)b

3a+(-2)b

3a-2b means that when merging similar terms, the swapped position sign remains unchanged, but the position is changed, and the number with the same letter and the same letter exponent (this is the same kind of term) is put together, and the concept of addition and subtraction of rational numbers learned in elementary school can be used to merge the similar terms after the swapping position. All you need to do is merge the same kind of items when you know the location. Just like the example just now.

But if you come across a bracketed one.

For example: 5 (a+3b)-3(3a+b).

5a+15b-(9a+27b)

5a+15b-9a-27b

5a-9a+15b-27b

4a+(-12)b

4a-12b

If you need to multiply it outside, that is, allocate it, then assign it first, and then remove the parentheses. When removing parentheses, remove parentheses conceptually:

If the parentheses are preceded by a "+" sign, remove the parentheses, and the items in the parentheses will not change;

If the parentheses are preceded by a "-" sign, remove the parentheses, and change the names of each item in the parentheses.

Got it? If you don't understand, feel free to ask.

This is what I wrote in detail myself).

1 There are two criteria for judging similar items: the letters contained are the same; The exponents of the same letter are also equal, and the two criteria are indispensable For example: 3x2 y and 3xy2 Although the letters contained are the same, in these two monomials, the exponents of x are not equal, and the number of values of y is not equal, so they are not of the same kind -2x3y and 3yx3 The two terms contain the same letters, and the exponents of the letters x and y are also equal, so they are similar terms 2 The main point of merging similar terms is:

The exponents of letters and letters remain unchanged; Add (merge) the coefficients of the same kind For example, if you combine the same terms 3x2y and 5x2y, the letters x, y and the exponents of x, y are all unchanged, just add their coefficients 3 and 5, i.e. 3x2y+5x2y=(3+5)x2y=8x2y I don't know which province you are from.

That's a very general question.

Merging terms of the same kind in a polynomial into one is called a merge of terms of the same kind (or merging terms of the same kind). The merging of terms of the same kind should be carried out according to the law: the coefficients of the same terms are added together, and the result is taken as a coefficient, and the letters and the exponents of the letters are unchanged.

For example, the multiplicative distributive property ab+ac=a(b+c).

As long as the number of letters is the same, you can add the previous coefficients.

For example: -6a 2b 3+9a 2b3=(-6+9)a 2b 3=3a 2b 3

This question is too broad, can you be specific?

First of all, if two monomials contain the same letters, and the exponents of each letter are also the same, then the two monomials are called homogeneous terms, and the merging of homogeneous terms in the polynomial into one is called the merger of homogeneous terms (or merging homogeneous terms)!

Merging terms of the same kind into one according to the distributive property of multiplication to addition is called merging terms of the same kind.

Rule: Merging similar terms is to add the coefficients of similar terms, and the result obtained is used as coefficients, and the letters and the exponents of letters remain unchanged.

The following two conditions should be met for the same kind of items:

1) The letters contained are the same;

2) Indices of the same letter are also the same.

The same kind of items not only contain the same letters, but also the indices of the same letters should be the same, regardless of the order of the letters, and have nothing to do with the coefficients; In addition, all constant terms are of the same kind.

Polynomials should contain terms with the same letters, and the same exponents of the same letters.

After merging similar items, the coefficients of the obtained items are the sum of the coefficients of the various items before the merger, and the letters and the exponents of the letters remain unchanged.

You can do it yourself, that's all I can help with.

If it is an excel sheet, you can directly combine it with the job number + name + group (each row uses a simple formula "= job number & name & group") to arrange the weight;

If it's a dbf table, it's even simpler, just use SQL statements.

Or do you want to sort?

The three tables are the same, just look at table one, and there is no need to merge.