"Factorization" Multiplication, division and factorization of integers PPT courseware 3

Description

"Factorization" Multiplication, division and factorization of integers PPT courseware 3

Question 1. Based on the experience and method of learning to use the square difference formula to decompose factors, analyze and speculate on what it means to use the perfect square formula to decompose factors?

Reverse the formula for the difference of squares for multiplication of integers to get the formula for the difference of squares from factorization. In the same way, the perfect square formula for multiplication of integers can be written in reverse to form the perfect square formula for factorization.

2. What are the characteristics of polynomials that can be factored using the perfect square formula?

The sum of the squares of two numbers, plus (or subtracting) 2 times the product of the two numbers, is equal to the square of the sum (or difference) of the two numbers.

Question 2: How to express the perfect square formula symbolically?

a2+2ab+b2=(a+b)2,

a2-2ab+b2=(a-b)2．

Method summary: The perfect square formula for decomposing factors. The left side is a quadratic trinomial, in which there is the sum of the squares of two numbers and twice the product of the two numbers or twice the product of the two numbers. If the opposite number meets these characteristics, it can be converted into the square of the sum (or difference) of the two numbers on the right. In order to achieve the purpose of factorization.

try one

1. Among the following polynomials, which one is in perfect square form ( )

A. x2-6x-9 B. a2-16a+3

C. x2-2xy+4y2 D. 4a2-4a+1

2. Which of the following polynomials is a correct factor ( )

A. 1+4x2=(1+2x)2

B. 6a-9-a2=-(a-3)2

C. 1+4m-4m2=(1-2m)2

D. x2+xy+y2=(x+y)2

3. Factoring:

(1)a2-10a+25

(2)-3x2+6xy-3y2

(3)3ax2+6axy+3ay2

(4)(a+b)2-12(a+b)+36

1: How to express the perfect square formula symbolically?

a2+2ab+b2=(a+b)2,

a2-2ab+b2(a-b)2．

2: What are the structural characteristics of the perfect square formula?

The perfect square formula for factoring, the left side is a quadratic trinomial, in which there is the sum of the squares of two numbers and 2 times the product of the two numbers or the opposite of 2 times the product of the two numbers, If it meets these characteristics, it can be converted into the square of the sum (or difference) of the two numbers on the right. In order to achieve the purpose of factorization.

Keywords: Multiplication, division and factorization of integers courseware, factoring courseware, New People's Education Edition eighth grade mathematics volume PPT courseware, eighth grade mathematics slide courseware download, multiplication, division and factorization of integers PPT courseware download, factorization PPT courseware download, .ppt format

For more information about the PPT courseware "Factorization of Integers: Multiplication, Division and Factorization", please click the "Factorization ppt Multiplication, Division and Factorization of Integers" ppt tag.

"Factorization" PPT courseware:

Contents of the first part of the PPT courseware "Factorization": Review of old knowledge 1. How many forms are there in multiplication of integers? (1) Multiplying a monomial by a monomial (2) Multiplying a monomial by a polynomial: m(a+b+c)=ma+mb+mc ( 3) Multiply a polynomial by a polynomial: (a+b)(m+n)=am+an+bm+bn 2. Multiplication common...

"Factorization" PPT:

"Factorization" PPT Part 1 Content: Fill in Can you find the connection and difference between these two sets of equations? What are the characteristics of their left and right sides? Features: Convert the form of the product of integers into the form of the sum of polynomials. Features: Convert the form of the sum of polynomials into...

"Factorization Method for Solving Quadratic Equations of One Variable" PPT courseware:

"Factorization Method for Solving Quadratic Equations" PPT courseware uses the factorization method to solve quadratic equations. General steps: (1) Change the right side of the equation to zero; (2) Decompose the left side of the equation into two linear equations. ________ of factors; (3) Let each factor be zero, we get..

File Info

Update Time: 2024-11-17

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 1 industry PPT template

Preview