"Perfect Square Formula" PPT Courseware 2

Description

"Perfect Square Formula" PPT Courseware 2

Mathematical expression of the perfect square formula:

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

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

Text description of the perfect square formula:

The square of the sum (or difference) of two numbers is equal to the sum of their squares plus (or minus) twice their product.

The geometric meaning of the perfect square formula

The perfect square formula for sum:

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

The perfect square formula for the difference:

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

Formula features:

1. The product is a quadratic trinomial;

2. The two terms in the product are the sum of the squares of the two numbers;

3. The other term is twice the product of the two numbers, and has the same sign as the middle of the multiplication.

4. The letters a and b in the formula can represent numbers, monomials and polynomials.

Think about it:

Are the calculations below correct? If it is incorrect, how should it be corrected?

(1)(x+y)2=x2+y2 Wrong (x +y)2 =x2+2xy +y2

(2)(x -y)2=x2 -y2 Wrong (x -y)2 =x2 -2xy +y2

(3)(-x +y)2 =x2+2xy +y2 Wrong (-x +y)2 =x2 -2xy +y2

(4)(2x+y)2 =4x2 +2xy +y2 Wrong (2x +y)2 =4x2+4xy +y2

Example 1: Calculate using the perfect square formula:

(1)(4m+n)2

Solution: (4m+n)2=(4m)2+2•(4m) •n+n2

=16m2+8mn+n2

(2)(x-2y)2

Solution: (x-2y)2=x2-2•x •2y+(2y)2

=x2-4xy+4y2

Example 2: Calculate using the perfect square formula:

(1) 1022

Solution: 1022= (100+2)2

=10000+400+4

=10404

(2) 992

Solution: 992

= (100 –1)2

=10000 -200+1

=9801

Class summary

1. Perfect square formula:

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

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

2. Pay attention to: the number of terms, symbols, letters and their exponents;

3. Commonly used conclusions when solving problems:

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

=(a-b)2+2ab

4ab=(a+b)2-(a-b)2

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"Perfect Square Formula" PPT courseware 3:

"Perfect Square Formula" PPT Courseware 3 Objective Navigation 1. Be proficient in using the perfect square formula for calculations; 2. Flexibly use the difference of squares and the perfect square formula to perform mixed operations; 3. Feel the power of the multiplication formula in the process of applying the multiplication formula for calculations. Function and...

"Perfect Square Formula" PPT courseware:

"Perfect Square Formula" PPT courseware review 1. Describe the content of the square difference formula and express it with letters. The product of the sum of two numbers and the difference of the two numbers is equal to the square difference of the two numbers. The formula is expressed as: (a+b ) (a-b)=a2 b2 2. 103 97=(100+3) (100-3) ..

"Perfect Square Formula" Operations of Integers PPT Courseware 3:

"Perfect Square Formula" Operations of Integers PPT Courseware 3 Activity 1 Explore and calculate what rules you can find in the following formulas? 1. (p+1)2 = (p+1) (p+1) = ______; 2. (m +2)2= _________; 3.(p-1)2 = (p-1 ) (p-1) = ________; 4.(..

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Update Time: 2024-06-30

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

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