How to calculate merging similar terms Find the formula for merging similar terms

Merging similar terms is the inverse multiplicative distributive property.

Combining a similar term in a polynomial is called merging similar terms.

If two monomials contain the same letters, and the exponents of each letter are the same, then the two monomials are said to be homogeneous. For example, 2AB and 3AB are the same term. In particular, all constant terms are also of the same kind.

Merging the same kind of terms in a polynomial into one term is called the merging of similar terms (or merging similar terms).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.

Steps: 1. Look for the same type.

2. Similar items are merged into one.

6ab-4ac+8ab-3ac

6+8)ab-(4+3)ab

Here, the symbol outside the parenthesis should be equal to the symbol in the original formula, that is, the symbol before the parenthesis should be assigned to each number in the parenthesis when opening the same kind of item, -(4+3)=-4-3, that is, -4 and -3

Remember, a negative sign touching a positive sign is negative, a negative negative is positive, and a negative sign touching a negative sign is positive.

For example, -8xy+3xy=-(8xy-3xy) is -8xy-(-3xy)=-8xy+3xy

4xy+2ab-3xy+4ab

4-3）xy+（2+4）ab=xy+6ab

Add the coefficients of the same kind (with symbols) and then copy the letters.

Swap positions with the previous symbols and calculate.

Knowing that they are of the same kind, you need to know that the order must be the same so m 3, (because it is followed by -3x to the power of 3, and you don't need to know the y after it).

Now that you know m 3

Then the original = 2009 times of (7*3-22).

21-22 times.

1) of 2009 times (the odd power of a negative number is known to be negative) Okay, that's it, you learned this, because you don't know what the power is, it's the power. Hope Sa.

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.

Merging similar terms is to use the multiplicative distribution law, the coefficients of similar terms are added, and the result is obtained as the number of the descendants, and the number of letters and fingers is 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.

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 the coefficient and another factor, since each term contains the same letter and their exponents are the same.

So each term of the same kind is the product of the coefficient and the same other factor. The distributive law is applied backwards when merging, multiplying the same factor by the algebraic sum of the coefficients.

Items that contain the same letters, and the exponents of the same letters are also the same, are called homogeneous terms.

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

Regarding the classification of algebraic formulas, it should be noted that:

1. To be classified according to the initial form given by the algebraic formula, e.g. (x +1) x +1 can be reduced to x +1, but it is still a fraction; For example, (x +1) -1 can be reduced to x2, but it is still irrational.

2. It is necessary to classify the operation of the specified variable digital master according to the buried cavity. For example, for variable nude x, the formula x+ a is rational, and the formula x+a is irrational.

Merge items of the same kind.

There is a theoretical basis for the law.

It is based on the well-known distributive law of multiplication.

a(b+c)=ab+ac。

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.

The operation of merging similar terms is based on the algorithm of polynomial addition and subtraction.

That is, if you add the terms with the same letters, the attention index should also be the same.

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: 3x y and 3xy, although they contain the same letters, in these two monomials, the exponents of x are not equal, y.

The number of values is also not equal, so it is not the same kind -2x 3y and 3yx both terms contain the same letters, and the exponents of the letters x and y are also equal, so they are of the same kind

2 The main points of merging similar terms are: the letters and the exponents of the letters remain unchanged; The coefficients of the same kind are added (combined). For example:

Combining the same terms 3x y and 5x y, the letters x, y and the exponents of x, y are all unchanged, as long as their coefficients 3 and 5 are added, i.e., 3x y + 5x y = (3 + 5) x y = 8x y