Integer mixed operation, integer mixed operation

a+b)(a-b)=a2-b 2 Example: (5+2) times (5-2)=5 2-2 2.

a+b)^2=a^2+2ab+b^2.(a-b)^2=a^2-2ab+b^2.

a-b)^2=a^2+2ab+b^2.(-a+b)^2=a^2-2ab+b^2.

Example: (5+2)=5 2+20+2 2(-5-2)=5^2+20+2^2.

If a -2a+1=0, then 2a -4a=

About the 2nd order trinomial of x, the 2nd term coefficient and the constant term are both 1, and the primary term coefficient is the opposite of four-thirds, please write this 2nd order 3nomial.

The quadratic trinomial of the polynomial (a -25) x -(a + 5) x + x + 3 Shi Guangyu x.

1) Find the values of the following formulas: a -4;②（a+2)(a-2);

2) What did you find out from the results of the two questions?

Specify a new operation, a b=a+b, a@b=a-b, where a, b are rational numbers, simplify the square of a * b 3ab + 5 * a square *b@4ab, and find what is the value when a = 5 and b = 3?

Knowing x-y=3, find the value of the algebraic equation 5-x+y+3(y-x).

1,3xy 〈6xy-3(xy-1/2x^2y)〉

2,(9x^2+2)(2x+1)

3,(-1-ab^2+a^2b^2/2).4a^2b

4,(1/4-2/3y^2)(-1/4x-2/3y^2)

Equation: 2x-1 2-2x+5 3=6x-7 6-1

x2+ax+b)(x2-3x+4)

x^4-3x^3+4x^2+ax^3-3ax^2+4ax+bx^2-3bx+4b

x^4-(3-a)x^3+(4-3a+b)x^2+(4a-3b)+4b

3-a=0 => a=3

4-3a+b=0

4-3*3+b=0

b=5 Let any of the 3 numbers x,y,z from 0 to 9 be taken.

The 6 two-digit numbers are: 10x+y, 10y+x, 10x+z, 10z+x, 10y+z, 10z+y.

Add 6 numbers together, and the sum is 22x+22y+22z=22(x+y+z).

Dividing by (x+y+z) equals 22.

So regardless of x, y, z, the end result is 22.

1)(x-y)(x+3) (2)

3)(5a2+8a)+(3a2-7a+5) (4)(-3)5•(-3)2•3

5) (6)x2y2•(-x2y)

7)(2a+3b)(a-b) (8)(5a3-2a+a2)÷(2a)

The square of a * b 3ab + the square of 5 * a * b@4ab

a^2*(b+3ab)+5a^2*(b-4ab)

a^2b+3a^3b+5a^2b-20a^3b

6a^2b-17a^3b

2x^2)^3-6x^3(x^3+2x^2+x)

8x^6)-(6x^6+12x^5+6x^4)

8x^6-6x^6-12x^5-6x^4

2x^6-12x^5-6x^4

x+y+z)(x+y-z)

x+y)^2 - z^2

x^2 + y^2 -2xy -z^2

x+y)^2-(x-y)^2]÷(2xy)

x^2 + 2xy + y^2 -(x^2 - 2xy + y^2)]/(2xy)

x^2 + 2xy + y^2 - x^2 + 2xy - y^2)]/(2xy)

4xy)/(2xy)

a^2 (a+1)^2-2(a^2-2a+4)

a^2[a^2 + 2a +1]-(2a^2-4a+8)

a^4 + 2a^3 + a^2 - 2a^2 + 4a -8

a^4 + 2a^3 - a^2 + 4a - 8

The algorithm of the four mixed operations of integers:

In the equation without parentheses.

, if there is only addition and subtraction or only multiplication and division, it should be calculated from left to right.

In an equation without parentheses, if there is both multiplication and division and addition and subtraction, multiplication and division must be calculated first, and then addition and subtraction.

In the formula with parentheses, the inside of the parentheses should be counted first, and then the inside of the middle brackets.

The meaning of the four operations

The rule of four operations

Although the rules for calculating the addition and subtraction of integers, decimals, and fractions are different, they all have one thing in common, that is, the addition or subtraction of numbers on the same unit of counting.

The law of integer multiplication:

Align the multiplier with the digit being multiplied.

Multiply the number on each digit of the multiplier from the single digit of the multiplier, and the last digit of the product multiplied by which digit should be aligned with the multiplier digit.

Finally, add up the product of several multiplications.

Multiplication of decimals:

The previous steps are exactly the same as integer multiplication, and finally see how many decimal places there are for the multiplier and multiplier, and count a few decimal places from the right side of the product to the left, and point to the decimal point.

Integer division rule:

Divide from the highest digit of the dividend, how many digits there are in the divisor, look at the first few digits of the dividend, if the dividend is smaller than the divisor, you need to look at one more place.

Divide to the digit of the dividend, and write the quotient on which digit.

Divide to which digit of the dividend is not quotient 1, write 0 above that digit.

The remainder of each division must be smaller than the divisor.

Decimal division rule: Decimal division is the same as integer division.

Fraction multiplication rule: two or more fractions are multiplied, the numerator multiplied by the numerator, and the denominator multiplied by the denominator is the denominator.

Fraction division rule: divide the number A by the number B (except 0), multiply the reciprocal of the number A by the number B, and then calculate according to the fraction multiplication.

The laws of arithmetic and simple algorithms

Four mixed operations

Addition and subtraction are called first-level operations, and multiplication and division are called second-level operations.

In an equation without parentheses, if it contains only the same level of operations, it should be calculated from left to right; If there are two levels of operations, the second level of operations should be counted first, and then the first level of operations.

In a formula with parentheses, the inside of the parentheses should be counted first, and then the inside of the middle brackets.

The four arithmetic algorithms, multiply and divide first, then add and subtract, first do the inside of the brackets, and do the outside of the brackets.

Four integers are mixed.

1.The four operations of addition, subtraction, multiplication, and division are collectively referred to as the four operations.

The meaning of addition: The operation of combining two (or several) numbers into one number is called addition.

The meaning of subtraction: It is known that the sum of two additions and one of them is called subtraction. In subtraction, the sum of two known additions is called the subtracted number, one of the additions is called the subtraction, and the other addition is called the difference.

The meaning of multiplication: multiplying a number by an integer is a simple operation to find the sum of several identical additions, or to find how many multiples of this number are.

The meaning of division: It is known that the product of two factors and one of the factors is called division. In division, the product of two known factors is called the dividend, one of the factors is called the divisor, and the other is called the quotient.

The four operations are divided into two levels, addition and subtraction are called first-level operations, and multiplication and division are called second-level operations.

2.Method: Tap:

The order of operations: In an equation without parentheses, if it contains only the same level of operations, it should be calculated from left to right; If there are two levels of operations, the second level of operations is counted first, and then the first level of operations. In the formula with parentheses, the ones in the parentheses should be counted first, and then the outside of the parentheses.

First calculate the square, then the parentheses, then the multiplication and division, and then the addition and subtraction.

1.The four mixed operation orders of integers: multiplication and division are calculated first, then addition and subtraction, and those with parentheses are counted first in parentheses.

2.Fraction addition and subtraction algorithm: add and subtract fractions with the same denominator, only add and subtract the numerator, and the denominator remains unchanged; Fractions with different denominators are added and subtracted, and the fractions with the same denominator are added or subtracted first.

3.The algorithm of fraction multiplication: use the product of the numerator as the numerator and the product of the denominator as the denominator.

4.The algorithm of fractional division: a number divided by a number that is not equal to 0 is equal to the reciprocal of multiplying this number.

5.The law of operation of integers:

Commutative law of addition: a b b a

Associative properties of addition: (a b) c a (b c) multiplicative commutative properties: a b b a

Multiplicative associativity: (a b) c a (b c).

In sibling operations, it is calculated from left to right; In the two-level operation, multiplication and division are calculated first, and then addition and subtraction; When there are parentheses, count the inside of the brackets first, and then the outside of the brackets; When there are multiple parentheses, the ones in the parentheses are counted first, and then the middle parentheses.

Inside, count the curly braces.

the inside, the last counts the outside of the parentheses; If there is a power.

Calculate the power first; In a mixed arithmetic, the number in parentheses is counted first, from small to large, and if there is a power, the power is counted first, and then from the advanced to the lowest.

The law of operation: 1. The commutative law of addition.

The two numbers are added to exchange the positions of the added numbers, and their sum does not change, i.e., a+b=b+a.

2. Associative law of addition.

Add the three numbers, add the first two numbers first, and add the third number; Or add the last two numbers first, and then add them to the first number, and their sum is unchanged, i.e., (a+b)+c=a+(b+c).

3. Multiplication commutative law.

When two numbers are multiplied, the position of the exchange factor and their product does not change, i.e., a*b=b*a.

4. Multiplication and associative law.

Multiply three numbers, first multiply the first two numbers, and then multiply by the third number; Or multiply the last two numbers first, and then multiply them with the first number, and their product remains the same, i.e., (a*b)*c=a*(b*c).

5. Multiplicative distributive law.

The sum of two numbers can be multiplied by one number, and the two additives can be multiplied by this number respectively and then added to the two products, that is, (a+b)*c=a*c+b*c.

The mixed operation of integers is as follows:

Integer: It is a part of a rational formula, in which it can contain four operations: addition, subtraction, multiplication, and division, but the dividend in an integer cannot contain letters. Monomials and polynomials are collectively referred to as integers.

A rational form in algebra. If there is no division operation or fraction, and although there are division operations and fractions, but the number of variable beams and sails is not included in the former parent of the division or division shout, it is called an integer. Integers contain monomials and polynomials (algebraic expressions with letters in the denominator are not integers).

The integer formula is calculated as follows:

1.The monomial is multiplied by the monomial, the product of the coefficient multiplied by the coefficient is the coefficient of the product, the base of the same letter is unchanged, the exponent is added, and the individual letters are unchanged, which is still a factor of the product.

2.Multiplying a monomial by a polynomial is to use a monomial to multiply each term of the polynomial and add all the terms.

3.First, multiply each term of one polynomial by each term of another polynomial, and then add the resulting product.

4.Numbers are divided by numbers, the same letters are divided, and for the letters that are only present in the dividend include the exponents of the letters as a factor of the quotient.

5.Divide the polynomial by the monomial, divide the polynomial by the monomial, and then add the resulting quotient.

6.General steps for dividing a polynomial by a polynomial: Dividing a polynomial by a polynomial, generally using vertical for calculus.

1) Arrange the divided, divided, and divided by a certain letter to the power of a certain letter, and fill in the missing items with zero;

2) Use the first term of the dividing formula to remove the first term of the dividing formula, and the first term of the quotient formula;

3) Use the first term of the quotient formula to multiply and divide, write the product below the dividable formula (alignment of similar terms), and subtract this product from the divided;

4) Take the difference subtracted as a new divided, and then continue to calculate according to the above method until the remainder is zero or the number of refractions is less than the number of divisions, the divided=dividing quotient + equivalent; If a polynomial is divided by another polynomial and the remainder is zero, the polynomial is said to be divisible by another polynomial;

5) If the divided formula can be factored and there is a factor that is the same as the factor in the dividing formula, the divided formula and the division formula can be factored. The most important thing is to pay attention to the symbols of the coefficients.

The four operations of the integer are as follows:

Integers can be divided into definitions and operations, definitions can be divided into monomials and polynomials, and operations can be divided into addition, subtraction, and multiplication and division. Addition and subtraction include merging similar terms, multiplication and division include basic operations, rules and formulas, basic operations can be divided into power operation properties, laws can be divided into integers, division, formulas can be divided into multiplication formulas, zero exponential powers and negative integer exponential powers.