"Perfect Square Formula" Operation of Integers PPT Courseware 3

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"Perfect Square Formula" Operation of Integers PPT Courseware 3

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"Perfect Square Formula" Operation of Integers PPT Courseware 3

Activity 1 Explore

Calculate the following equations, what patterns can you find?

1.(p+1)2 = (p+1) (p+1) = ______;

2.(m+2)2= _________;

3.(p-1)2 = (p-1 ) (p-1) = ________;

4.(m-2)2 = __________.

Activity 2 Calculate (a+b)2, (a-b)2

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

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

Activity 3

Generally, we have

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

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

That is, the square of the sum (or difference) of two numbers is equal to the sum of their squares, plus (or subtracting) 2 times their product. These two formulas are called (multiplicative) perfect square formulas.

Example: Calculate using the perfect square formula:

(1) 1022; (2) 992.

Solution: (1)1022 = (100 +2) 2

= 1002 +2×100×2 + 22

= 10000 +400 +4

= 10404;

(2)992 = (100 -1)2

= 1002 -2×100×1+12

= 10000 - 200 + 1

= 9801.

practise

1. Use the perfect square formula to calculate:

(1)(x+6)2; (2) (y-5)2;

(3) (-2x+5)2; (4) (3/4x -2/3y)2.

2. What are the errors in the following calculations? How should they be corrected?

(1) (a+ b)2 = a2 +b2;

(2) (a – b) 2 =a2 – b2.

The rule of adding brackets

a+(b+c) = a+b+c; a- (b+c) = a - b – c.

a + b + c = a + ( b + c) ; a – b – c = a – ( b + c ) .

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.

practise

1. Fill in the appropriate terms in the brackets to the right of the equal sign:

(1) a + b + c = a + ( );

(2) a – b – c = a – ( ) ;

(3) a – b + c = a – ( );

(4) a + b + c = a – ( ).

2. Use the multiplication formula to calculate:

(1) (a + 2b – 1 ) 2;

(2) (2x +y +z ) (2x – y – z ).

3. As shown in the figure, from a circular steel plate with diameter a+b, two circles with diameters a and b are dug out from it, and find the area of ​​the remaining steel plate.

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For more information about the PPT courseware "Operations of Integers with Complete Square Formulas", please click the "Operations of Integers with Complete Square Formulas ppt" ppt tag.

"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 2:

"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 sum of two numbers (or difference) squared, is equal to the sum of their squares, plus (or minus..

"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) ..

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