The first volume of eighth grade mathematics courseware
Polynomial divided by monomial
First, the learning objectives:
The algorithm of 1. polynomial divided by single term and its application.
2. The algorithm of polynomial divided by monomial.
Second, the key difficulties:
Two-point: Polynomial Divided by Single Term Algorithm and Its Application
Difficulties: Explore the process of division algorithm between polynomial and monomial.
Third, cooperative learning:
(1) Review the law of dividing the monomial by the monomial.
(B) students began to explore new courses.
1. Calculate the following:
( 1)(am+BM)÷m(2)(a2+ab)÷a(3)(4x2y+2xy 2)÷2xy。
2. Question: ① Tell me how you worked it out ② What else did you find?
(3) Summary rules
1. Polynomial divided by monomial: first divide each term of this polynomial by _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
2. Essence: Divide the polynomial by the monomial and convert it into _ _ _ _ _ _ _ _ _ _ _ _
Fourth, diligence and conciseness
Example: (1) (12a3-6a2+3a) ÷ 3a; (2)(2 1x4y 3-35x3y 2+7x2y 2)÷(-7x2y)；
(3)[(x+y)2-y(2x+y)-8x]÷2x(4)(-6a3b 3+8a2b 4+ 10a2b 3+2ab 2)； (-2ab 2)
Classroom exercises: textbook exercises
Verb (abbreviation of verb) abstract
1, the division rule of monomial
2, the application of single division should pay attention to:
A, divide by the coefficient first, and the result is taken as the coefficient of quotient. Note that the coefficients of individual items are all preceded by symbols.
B, divided by the same base, the result is the factor of quotient. Because only the divisibility is studied at present, the index of a letter in the divisibility formula is not less than that of the same letter in the divisibility formula;
C, separate types of letters and their indexes, as a factor of quotient, should not be omitted;
D, pay attention to the operation sequence. Those who have power should do power first, and those with brackets should do the same level operation from left to right.
E, polynomial divided by monomial rule
formula for the difference of square
First, the learning objectives:
1. Go through the process of exploring the square difference formula.
2. Can deduce the square difference formula, and can use the formula for simple operation.
Second, the key points and difficulties
Derivation and application of square difference formula
Difficulties: understand the structural characteristics of the square difference formula and use it flexibly.
Third, cooperative learning.
Can you calculate the following questions in a simple way?
( 1)200 1× 1999 (2)998× 1002
Introduce a new lesson: Calculate the product of the following polynomials.
( 1)(x+ 1)(x- 1)(2)(m+2)(m-2)
(3)(2x+ 1)(2x- 1)(4)(x+5y)(x-5y)
Conclusion: The product of the sum of two numbers and the difference of these two numbers is equal to the square difference of these two numbers.
Namely: (a+b)(a-b)=a2-b2.
Fourth, diligence and conciseness
Example 1: Calculated by square difference formula:
( 1)(3x+2)(3x-2)(2)(b+2a)(2a-b)(3)(-x+2y)(-x-2y)
Example 2: Calculation:
( 1) 102×98(2)(y+2)(y-2)-(y- 1)(y+5)