"Formula of Square Differences" PPT download of multiplication and division of integers

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"Formula of Square Differences" PPT download of multiplication and division of integers

Part 1: Polynomials and Polynomial Multiplication

First multiply each term of one polynomial by each term of the other polynomial, and then add the resulting products.

(m+a)(n+b)=mn+mb+an+ab

Calculate each of the following questions:

(1) (x+3)(x−3)

(2) (1+2a)(1−2a)

(3) (x+4y)(x−4y)

(4) (y+5z)(y−5z)

(a+b)(a−b)=x2−b2

Characteristic structure

(1) The two binomials on the left side of the formula must be the product of the sum and difference of the same two numbers;

And the first term in the two brackets on the left is equal and the sign of the second term is opposite[They are opposite numbers (formula)];

(2) The right side of the formula is the square difference of these two numbers;

That is, the right-hand 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 represent numbers or algebraic expressions.

Square Difference Formula PPT, Part 2: Analysis of Examples

Example 1: Calculate using the square difference formula:

(1) (5+6x)(5−6x); (2) (x+2y)(x−2y); (3) (−m+n)(−m−n).

When the "first (second) number" is a fraction or the product of a number and a letter, the entire number must be enclosed in parentheses and then squared; the parentheses must be removed from the final result.

Example 2: Calculate using the squared difference formula:

Observe the following equations and then answer the questions: 1×3+1=4=22, 3×5+1=16=42, 5×7+1=36=62,…

(1) Please use an equation containing n to express the law of the above equation (n is a positive integer);

(2) Please prove the equation you wrote.

(1) Solution: ∵1×3+1=4=22, 3×5+1=16=42, 5×7+1=36=62,…,

∴Use an equation containing n to express the above equation as follows: (2n-1) (2n+1)+1=(2n)2;

(2) Prove: (2n-1) (2n+1)+1= (2n)2-1+1= (2n)2.

Keywords: Beijing Normal University version seventh grade mathematics volume 2 free download PPT courseware, square difference formula PPT download, multiplication and division of integers PPT download, .PPT format;

For more information about the PPT courseware "Formula for Multiplication and Division of Square Differences of Integers", please click on the PPT tab of "Formula for Multiplication and Division of Square Differences of Integers".

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Update Time: 2024-11-22

This template belongs to Mathematics courseware Beijing Normal University Edition Seventh Grade Mathematics Volume 2 industry PPT template

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