"Factorization using common factor method" PPT courseware 2

Description

"Factorization using common factor method" PPT courseware 2

Collaboration and inquiry

1. Find the product of the following integer multiplications:

①, m(a+b+c)=ma+mb+mc

②、5y2(y+4)=5y3+20y2

2. I believe you can quickly tell the following results:

①、ma+mb+mc=m(a+b+c)

②、5y3+20y2=5y2(y+4)

Factorization: converting a polynomial into the product of several integers.

Factoring and multiplication of integers have a reciprocal relationship.

The above method of factorization is called the common factor method.

Exercise 1 Understand the concepts

Determine which of the following expressions are integer multiplications? Which ones are factoring?

(1).x2-4y2=(x+2y)(x-2y)

(2).2x(x-3y)=2x2-6xy

(3).(5a-1)2=25a2-10a+1

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

(5).(a-3)(a+3)=a2-9

(6).m2-4=(m+4)(m-4)

(7).2 πR+ 2 πr= 2 π(R+r)

Debate with fiery eyes and golden eyes

Decide which of the following are factorizations and explain why

(1)x2_3x+2=x(x-3)+2

(2)3a2+6a=3a(a+2)

(3)2m(m+n)=2m2 +2mn

Explore new knowledge

Find the same factors in each of the following polynomials:

1.am+bm+cm

2. 12m2-4m3

3. 5x2y-10xy

Common factor: The same factor that all terms in a polynomial contain.

How to find common factors:

1. Definite coefficients: When each coefficient is an integer, find the (greatest common divisor) of each coefficient

2. Definite letters: Take the letters that are contained in each term of the polynomial (the same letter).

3. Fixed exponent: take the exponent of the same letter (lowest power).

Example 1: Factor the following expressions:

(1)3a2+12a; (2)-4x2y-16xy+8x2.

Solution: (1) 3a2+12a

=3a.a+3a.4

=3a(a+4)

(2)-4x2 -16xy+8x2

=-4x(x+4y-2x)

Students should note:

(1) All common factors must be mentioned and cannot be omitted

(2) When the first coefficient of the polynomial is a negative number, the "-" sign is usually raised first to make the first coefficient in the brackets become a positive number. Note that the signs of each term in the brackets must be changed.

1.What is factorization?

2. How to determine common factors?

(1) Definite coefficient (2) Definite letter (3) Definite exponent

3. What are the steps to decompose factors using the common factor method?

(1) Find common factors (2) Propose common factors

4. What should we pay attention to when formulating common factors?

(1) Mention all the common factors (2) Be careful to omit them (3) When the first term of the polynomial is a negative number, you usually have to mention the sign first, and pay attention to the sign change of each term in the brackets.

feedback detection

1: (1)—7xy-14xyz2+49xyz=-7xy( )

(2) Factorization: x(a-y)-y(y-a)=( )

(3) Factorization: (2x-y)-(y-2x)2=( )

(4) Calculation: 39x37-13x34=( )

2. Factoring

(1)6a3-8a2-4a

(2)18(b-a)2-12(a-b)3

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

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"Using Common Factor Method to Factorize" PPT courseware:

"Using the Common Factor Method to Factorize" PPT courseware communication and discovery: Find the same factors contained in each term of the following polynomials: 1. am+bm+cm m 2. 12m2-4m3 4m2 3. 5x2y- 10xy 5xy Common Factors: All terms in a polynomial have the same factor..

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Update Time: 2024-10-14

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 2 industry PPT template

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