First, the essence of the operation of reverse power.

1.。

2.( )2002×( 1.5)2003÷(- 1)2004=________。

3. If, then.

4. Known:, the value of,.

5. Given:,, then = _ _ _ _ _.

Second, the formula deformation evaluation

1. If, then.

2. We know the values of, and.

3. Known, the value of.

4. If: known, then =.

5. As a result.

6. If (2a+2b+1) (2a+2b-1) = 63, then the value of a+b is _ _ _ _ _ _ _ _.

7. Known:,,,

The value.

8. If so.

9. Known, the value of.

10. If known, the value of the algebraic expression is _ _ _ _ _ _ _ _ _.

1 1. If: known, then _ _ _ _ _ _ _ _ _ _.

Thirdly, the formula is deformed to judge the shape of triangle.

1. It is known that,, and are three sides of a triangle, and satisfy, then the shape of the triangle is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

2. If the lengths of three sides of a triangle are,,, then the triangle is _ _ _ _ _ _ _ _ _ _ _ _ _ _.

3. It is known that,, are three sides of △ABC and satisfy the relation. Try to judge the shape of △ABC.

Fourth, the factors of grouping decomposition

1. Decomposition factor: A2-1+B2-2ab = _ _ _ _ _ _ _ _ _.

2. Decomposition factor: _ _ _ _ _ _ _ _ _ _.

Verb (short for verb) others

1. It is known that m2 = n+2, N2 = m+2 (m ≠ n), and find the value of m3-2mn+n3.

2. Calculation:

Review of algebraic expressions in seventh grade.

A. monomials and polynomials are collectively called algebraic expressions.

B. Algebraic expressions are rational expressions that do not contain division operations or fractions, and that do not contain variables in division or denominator. If there is a division operation with letters, then the formula is called fractional decimal. )

C algebraic expressions can be divided into definitions and operations, definitions can be divided into monomials and polynomials, and operations can be divided into addition, subtraction, multiplication and division.

D addition and subtraction include merging similar terms, multiplication and division include basic operations, rules and formulas, and basic operations can be divided into power operations. Rules can be divided into algebra and division, and formulas can be divided into multiplication formula, zero exponential power and negative integer exponential power.

Algebraic expressions and similar items

1. Single item

The expression of (1) monomial: 1, the product of a number and a letter. This algebraic expression is called monomial 2, and a single letter is also a monomial.

3. A number is a monomial. 4. Letters multiplied by letters form a monomial. 5. Multiply numbers to form a monomial.

(2) Single coefficient: the numerical factors and property symbols in a single item are called single coefficient.

If a single item contains only numerical factors, the positive single item coefficient is 1 and the negative single item coefficient is-1.

(3) The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.

2.polynomial

The concept of (1) polynomial: The sum of several monomials is called polynomial. In polynomials, each monomial is called a polynomial term, and the term without letters is called a constant term. Polynomials with several terms are called polynomials. The symbols in polynomials are regarded as the natural symbols of each term. A univariate polynomial of degree n can have at most N+ 1 terms.

(2) Degree of Polynomial: The degree of the term with the highest degree in the polynomial is the degree of the polynomial.

(3) the arrangement of polynomials:

1. Sorting polynomials in descending alphabetical order is called sorting polynomials in descending alphabetical order. 2. Arranging a polynomial according to the exponent of a letter from small to large is called arranging polynomials according to the ascending power of this letter.

Since a polynomial is the sum of several monomials, the position of each term can be exchanged by the addition algorithm, while keeping the value of the original polynomial unchanged.

In order to facilitate the calculation of polynomials, a polynomial is usually arranged in a neat and simple form in a certain order, which is the arrangement of polynomials.

Pay attention to when doing polynomial arrangement problems:

(1) Since a single item contains its preceding attribute symbol, the attribute symbol of each item should still be regarded as a part of the item and moved together.

(2) The arrangement of polynomials with two or more letters should pay attention to:

A. first of all, it must be arranged according to the index of which letter.

B. determine whether to arrange letters inward or outward.

(3) Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.

(4) the concept of similar items:

Items with the same letters and times are called similar items, and several constant items are also called similar items.

When mastering the concept of similar items, we should pay attention to:

1. To judge whether several monomials or terms are similar, two conditions must be mastered:

(1) contains the same letters.

The same letter has the same number of times.

2. Similar items have nothing to do with coefficient or alphabetical order.

3. Several constant terms are similar.

(5) Merge similar items:

1. The concept of merging similar projects:

Merging similar terms in polynomials into one term is called merging similar terms.

2. Rules for merging similar projects:

The coefficients of similar items are added together, and the results are taken as coefficients, and the indexes of letters and letters remain unchanged.

3. To merge similar projects:

(1). Find similar projects accurately.

(2) Reverse the distribution law, add the coefficients of similar items together (enclosed in brackets), and keep the letters and their indices unchanged.

(3) Write the merged result.

When mastering the merger of similar projects, we should pay attention to:

1. If the coefficients of two similar items are opposite, the result after merging similar items is 0.

2. Don't leave out items that can't be merged.

3. As long as there are no more similar items, it is the result (either a single item or a polynomial).

The key to merging similar items: correctly judging similar items.

Algebraic expression and multiplication of algebraic expression

Algebraic expressions can be divided into definitions and operations, definitions can be divided into monomials and polynomials, and operations can be divided into addition, subtraction, multiplication and division.

Addition and subtraction involve merging similar items. Multiplication and division include basic operations, rules and formulas. Basic operations can be divided into power operations. Rules can be divided into algebra and division, and formulas can be divided into multiplication formula, zero exponential power and negative integer exponential power.

The power rule of the same base: multiply with the power of the same base and add with the index of the same base.

Power law: power, constant basis, exponential multiplication.

Power law of product: the power of product is equal to the power obtained by multiplying the factors of product respectively and then multiplying them.

The multiplication of monomials and monomials has the following rules: the monomials are multiplied by their coefficients and the same base respectively, and other letters and their exponents are kept as the factorial of the product.

There are the following rules for the multiplication of monomial and polynomial: the multiplication of monomial and polynomial is to multiply each term of polynomial with monomial, and then add the products.

Polynomial and polynomial multiplication have the following rules: polynomial and polynomial multiplication, first multiply each term of one polynomial with each term of another polynomial, and then add the obtained products.

Square difference formula: the product of the sum of two numbers and the difference between these two numbers is equal to the square difference between these two numbers.

Complete square formula: the square of the sum of two numbers is equal to the sum of the squares of these two numbers, plus twice the product of these two numbers. The square of the difference between two numbers is equal to the sum of the squares of these two numbers, MINUS twice the product of these two numbers.

Same base powers divides, the base remains the same, and the exponent is subtracted.

Final algebraic expression review questions

First, multiple-choice questions.

Calculate (-3)2n+ 1+3? The correct result of (-3)2n is ()

A.32n+2 B. -32n+2 C. 0 D. 1

2. There are five propositions as follows: 13A2+5A2 = 8A22M2? m2=2m2 ③x3？ x4=x 12 ④(-3)4？ (-3)2=-36 ⑤(x-y)2？ (y-x)3=(y-x)5. The number of correct propositions is ().

A. 1 B. 2 C. 3 D.4

3. The value of x for 2x (x-1)-x (2x-5) =12 is ().

A.x= 1 B. x=2 C. x=4 D. x=0

4. Let (5a+3b)2=(5a-3b)2+M, then the value of m is ().

A.30ab b . 60ab c . 15ab d . 12ab

5. Given xa=3 xb=5, the value of x3a+2b is ().

A. 675 BC to 52 BC

6. The relationship between-an and (-a)n is ().

A. Equality

B. reciprocal

C. when n is odd, they are equal; When n is even, they are reciprocal.

D. when n is odd, they are reciprocal; When n is an even number, they are equal.

7. The following calculation is correct ()

Answer. (-4x)(2 x2+3x- 1)=-8x 3- 12 x2-4x b .(x+y)(x2+y2)= x3+y3

C.(-4a- 1)(4a- 1)= 1- 16 a2 d .(x-2y)2 = x2-2xy+4 y2

8. The following deformation from left to right, belongs to the factorization is ().

A.(x+ 1)(x- 1)=-x2- 1 b . x2-2x+ 1 = x(x-2)+ 1

C.a2-B2 =(a+b)(a-b)d . MX+my+NX+ny =(x+y)m+n(x+y)

9. If x2+mx- 15=(x+3)(x+n), the value of m is ().

A.-5b 5c-2d 2

10.4 (a-b) 2-4 (b-a)+1The result of factorization is ().

A.(2a-2 b+ 1)2 b .(2a+2 b+ 1)2

C.(2a-2 b- 1)2d .(2a-2 b+ 1)(2a-2 b- 1)

Fill in the blanks.

1 1. Calculate 3 xy2(-2xy)= 1

12. The common factor of the polynomial 6x2y-2xy3+4xyz is

13. If the polynomial (mx+8)(2-3x) does not contain x term after expansion, then m=

14. Let 4x2+mx+ 12 1 be completely flat, then m=

15. given A+B = 7, AB = 12, a2+b2=

Three. Answer questions (***55 points)

16. Calculate (a2)4a-(a3)2a3.

17. Calculation (5a3b) (-4abc) (-5ab)

18. It is known that 22n+ 1+4n=48. Find the value of n.

19. Simplify first and then seek (x+3)(x-4)-x(x-2), where x= 1 1.

20. Use the multiplication formula to calculate

( 1) 1.02×0.98 (2) 992

2 1. Factorization 4x- 16x3

22. Factorization 4a(b-a)-b2

23. Given (x+my)(x+ny)=x2+2xy-6y2, how about -(m+n)? Value of mn

24. given A+B = 3 and AB =- 12, find the following values.

( 1) a2+b2 (2) a2-ab+b2

Additional questions.

1. Can you explain why the values of algebraic expressions n (n+7)-(n-3)-(n-2) are divisible by 6 for any natural number n?

2. It is known that A, B and C are the trilateral lengths of △ a, B and C, which satisfy:

A2+2b2+c2-2b(a+c)=0。 Try to judge the shape of this triangle.

Answers to the final algebraic expression review questions.

A multiple-choice questions (* * 10 questions, 3 points for each small question ***30 points)

1.c，2。 B 3。 C 4 explosive B 5。 B 6。 C 7。 C 8。 C 9。 C 10。 A

2. Fill in the blanks (3 points for each question *** 15 points)

1 1.-6x2y3 12。 2xy(3x-y2+2z) 13。 12 14.44 15.25

Three. Answer questions (***55 points)

16. solution: original formula =a8a-a6a3= a9-a9= 0.

17. solution: original formula = (-20a4b2c) (-5ab) =100a5b3c.

18. Solution: 22n+1+4n = 48 22n2+22n = 48 22n (1+2) = 48 22n =16 22n = 24n = 2.

19. Solution: Original formula =x2-4x+3x- 12-x2+2x.

=x- 12

Substitute X= 1 1 into x- 12 to get:

x- 12=- 1

20.( 1) solution: the original formula = (1+0.02) (1-0.02) =1-0.004 = 0.9996.

(2) Solution: The original formula = (100-1) 2 =10000-200+1= 9801.

2 1. solution: original formula = 4x (1-4x2) = (1+2x) (1-2x).

22. solution: the original formula = 4ab-4a2-B2 =-(4a2-4ab+B2) =-(2a-b) 2.

23. solution: (x+my)(x+ny)=x2+2xy-6y2,

x2+(m+n)xy+mny2= x2+2xy-6y2

Namely: m+n=2 mn=-6.

-( m+n) mn=(-2) (-6)= 12

24.( 1) Solution: a2+b2

= a2+2ab+b2 -2ab

=(a+b) 2- 2ab

Substituting a+b = 3 and ab =- 12 into (a+b) 2- 2ab, we get:

(a+b) 2- 2ab=9+24=33

(2) Solution: a2-ab+b2

= a2-ab+3ab+ b2-3ab

= a2+2ab+b2 -3ab

=(a+b) 2-3ab

Substituting A+B = 3 and AB =- 12 into (a+b) 2- 3ab, we get:

(a+b) 2- 3ab=9+36=45

Additional questions (10, 5 points for each question)

Solution: n (n+7)-(n-3) (n-2) = N2+7N-(N2-5N+6)

= N2+7n-N2+5n-6 = 12n-6 = 6(2n- 1)

That is, the values of algebraic expressions n (n+7)-(n-3)-(n-2) can be divisible by 6.

Solution: A2+2b2+C2-2b (a+c) = 0a2+B2+B2+C2-2ba-2bc = 0.

(a-b) 2+(b-c) 2=0, that is, A-B = 0, B-C = 0 A = B = C.

So △ABC is an equilateral triangle.