"Square Difference Formula" Operation of Integers PPT Courseware 3

Description

"Square Difference Formula" Operation of Integers PPT Courseware 3

teaching objectives

knowledge and abilities

1. Understand the meaning of the square difference formula;

2. Master the structural characteristics of the square difference formula;

3． Correctly use the squared difference formula to calculate;

4. The rule of adding brackets;

5. Use the bracketing rule to flexibly apply the squared difference formula.

Process and Method

1. Experience the process of exploring the squared difference formula, be able to derive the squared difference formula, and be able to use the formula to perform simple operations;

2. In the process of exploring the square difference formula, develop symbolic sense and reasoning ability;

3． Cultivate reverse thinking ability through the rules of adding brackets and removing brackets.

Emotional attitudes and values

1. Discover patterns in the calculation process and be able to express them with symbols, thereby experiencing the simplicity and beauty of mathematics;

2. Diversify algorithms, cultivate the habit of thinking about problems in multiple aspects, and improve the awareness of cooperation and communication and the spirit of innovation.

Important and difficult points in teaching

focus

1. Derivation and application of the squared difference formula;

2. Master the structural characteristics of formulas and correctly use formulas;

3． Understand the rules of adding parentheses and become more familiar with the rational use of multiplication formulas.

difficulty

1. Understanding of the process of formula derivation from general to specific;

2. Use formulas correctly and understand the broad meanings of letters in formulas;

3． Understand the structural characteristics of the squared difference formula and flexibly apply the squared difference formula;

4. How to add parentheses appropriately in the multiplication of polynomials and polynomials to achieve the purpose of applying formulas.

Calculate the product of the following polynomials.

(1) (x+6) (x-6)

(2) (m+5)(m-5)

(3) (5x+2) (5x-2)

(4) (x+4y) (x-4y)

Observing the above polynomials, what patterns did you find? After calculating the results, what patterns did you discover?

calculate

(1)(x+3)(x−3) =x2−9 =x2−32;

(2) (1+2a)(1−2a) =1−4a2=12−(2a)2;

(3) (x+4y)(x−4y) =x2−16y2 =x2−(4y)2;

(4) (y+5z)(y−5z) =y2−25z2 =y2−(5z)2 ．

For multiplication of polynomials with special forms like this, can we find a general formula and memorize it so that when we encounter multiplication of polynomials of the same form, we can directly write out the results?

Knowledge points

Generally, we have

(a+b)(a-b)=a2-b2

That is, the product of the sum of two numbers and the difference of the two numbers is equal to the squared difference of the two numbers.

This formula is called the (multiplicative) squared difference formula.

Structural features of the squared difference formula

(a+b)(a−b)=a2−b2

(1) The two binomials on the left side of the formula must be the sum and difference of the same two numbers multiplied; and the first term in the two brackets on the left is equal and the second term has opposite signs (they are opposite numbers or formulas.

(2) The right side of the formula is the square difference of these two numbers; that is, the right side is the square of the first term in the left bracket minus the square of the second term.

(3) a and b in the formula can be numbers or algebraic expressions.

(4) The number of terms in each factor is the same. Those with the same sign are placed in the front and squared, and those with opposite signs are placed in the back and squared.

Example 1: Calculate using the square difference formula:

(1)(7+6x)(7−6x);

(2)(3y + x)(x−3y);

(3) (−m＋2n)(−m−2n).

Solution: (1) (7+6x)(7−6x)=72-(6x)2=49-36x2

(2) (3y+x) (x−3y) =x2－3y2=x2－9y2

(3) (−m+2n)(−m−2n )=(－m)2－(2n)2=m2－4n2

Example 3 Determine whether the following formula can be calculated using the squared difference formula:

(1) (a+2b)(a−2b); (cannot) (the first number is not exactly the same)

(2) (a−2b)(2b−a); (cannot)

(3) (2a+b)(b+2a); (cannot)

(4) (a−3b)(a+3b); (energy) −(a2 −9b2)= −a2 + 9b2 ;

(5) (2x+3y)(3y−2x). (cannot)

Knowledge points

Rules for adding parentheses:

When adding parentheses, if there is a positive sign in front of the parenthesis, the signs of the items enclosed in the parentheses will not change; if there is a negative sign in front of the parentheses, the signs of the items enclosed in the parentheses will change.

In other words, it does not change when it encounters "addition", but changes when it encounters "subtraction".

practice

(3a＋b+c)(3a＋b－c)

=[(3a＋b) +c][(3a+b) -c]

=(3a+b)2-c2

=9a2+6ab+b2-c2

Class summary

squared difference formula

(a+b)(a−b)=a2−b2

The product of the sum of two numbers and the difference of the two numbers is equal to their squared difference.

For those that do not conform to the standard form of the square difference formula, or to extract the "-" sign from the two "-" signs, the commutative law of addition must be used to change it into the standard form of the formula before using the formula.

Keywords: teaching courseware for the operation of integers, teaching courseware for the square difference formula, Beijing Normal University edition seventh-grade mathematics second volume PPT courseware, download of the seventh-grade mathematics slide courseware, downloading the operation PPT courseware for the integer, downloading the squared difference formula PPT courseware,. ppt format

For more information about the PPT courseware "Operations of Square Difference Formulas and Integers", please click the "Operations of Square Differences Formula ppt Integers" ppt tag.

"Formula of Squared Differences" PPT courseware 2:

"Formula of Square Differences" PPT Courseware 2 How do polynomials multiply? (a+b)(m+n)=am+an+bm+bn (x + 1)( x-1) =x2-1x+1X-11 =x2-1 Calculate and compare to see who can calculate better Calculate the following questions quickly and accurately ① (x +..

"Formula of Square Differences" PPT courseware:

"Formula of Square Differences" PPT courseware. Can you answer the multiplication rule of polynomials? (a+b)(m+n)=am+an+bm+bn Calculate and compare to see who can calculate faster and more accurately ( a+b)(a-b)=a2-b2 ①(x+2)( x-2) ②(1+3a)( 1-3a) ③(m+5n)( m..

"Square Difference Formula" Operation of Integers PPT Courseware 2:

"Formula of Squared Differences" Operation of Integers PPT Courseware 2 1. Analysis of teaching materials 1. The status and role of teaching materials; 2. Key points and difficulties of teaching; 3. Objectives of teaching; The status and role of the formula of squared differences of teaching materials is both the student's understanding of the previous Learn to combine similar terms and polynomials..

File Info

Update Time: 2024-10-20

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

Preview