"Using Formula Method to Factorize" PPT Courseware 2

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"Using Formula Method to Factorize" PPT Courseware 2

Use your brain to answer the following questions:

1 What is factorization? What is the factoring method we have learned?

2 What are the differences and connections between factorization and integer multiplication?

3 Can you factor m2-4, m2+4m+4?

Complete the blanks below and think about:

(1) Calculated according to the multiplication formula:

①(m+2)(m-2)＝ ②(a+b)(a-b)=

③(m+2)2= ④(a+b)2=

(2) Fill in the blanks based on the symmetry of the equation

①m2-4= ②a2-b2=

③m2+4m+4= ④a2+2ab+b2=

(3) Thinking:

1. Are the transformations of the four polynomials in (2) factorization?

2. What do you find by comparing (1) and (2)?

Explore the structural features of formulas

1. Which of the following polynomials can be factored using the square difference formula?

①x2-y2; ②-x2+y2; ③x2+y2; ④-x2-y2; ⑤16-b2.

Discussion: When factoring, what are the characteristics of the square difference formula a2-b2=(a+b)(a-b)?

2. Which of the following polynomials can be factored using the perfect square formula?

①x2+2xy+y2; ②-x2+2xy+y2;

③x2+xy+y2; ④x2-xy+y2.

Discussion: When factoring, what are the characteristics of the perfect square formula a2+2ab+b2=(a+b)2?

Structural features of the squared difference formula:

(1) The left side is a binomial, each term is in the form of a square, and the signs of the two terms are opposite;

(2) The right side is the product of two polynomials. One factor is the sum of the two numbers, and the other factor is the difference between the two numbers.

Structural features of the perfect square formula:

(1) On the left is a trinomial. Two terms are positive and can be written in square form. The other term is twice the product of two bases just written as a square term.

(2) The right hand side is the square of the sum of the bases of the two square terms.

Factor the following expressions:

(1) 4x2-16y2 (2)x2+2xy+y2.

Solution: Original formula = 4(x2-4y2) Solution: Original formula = (x2+2xy+y2)

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

⑶ -x3y3-2x2y2-xy (4)81a4-b4

Solution: Original formula=-xy(x2y2+2xy+1) Solution: Original formula=(9a2+b2)(9a2-b2)

=-xy(xy+1)2 =(9a2+b2)(3a+b)(3a-b)

⑸(2x+y)2-2(2x+y)+1

Solution: Original formula = (2x+y-1)2

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"Using Formula Method to Factorize" PPT courseware:

"Using Formula Method for Factorization" PPT courseware Learning objectives: 1. Understand the meaning of the square difference formula and the perfect square formula in factorization. 2. Be able to factor polynomials using the formula method. 3. Understand the general steps of factorization. Key points to learn..

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Update Time: 2024-11-20

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

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