( 1)59.8×60.2;

The original formula = (60-0.2) (60+0.2) = 3600-0.04 = 3599.96.

(2)2009? -2008×20 10;

Original formula = (2010-1) (2008+1)-2008× 2010.

=20 10-2008- 1

= 1

(3)99× 10 1× 1000 1.

Original formula = (100-1) (100+1) (10000+1)

=( 10000- 1)( 10000+ 1)

= 100000000- 1

=9999999

2. known x? -Really? =6, x+y=3, find the value of x-y.

Solution: x? -Really? =(x+y)(x-y)=3(x-y)=6

x-y=2

2. Observe the following types and explore the law:

1×3=3=2? - 1; 3×5= 15=4? - 1;

5×7=35=6? - 1; 7×9=63=8? - 1

9× 1 1=99= 10? - 1; ......

Use an equation of positive integer n to express the law you found:

n(2n+ 1)=(2n)2- 1

Three. Multiple choice problem

1.(x-y-3)？ +(x-y+5)？ =0, then x? -Really? The value of =0 is ()

a . 8 B- 8 c . 15d .- 15

Solution: (x-y) 2-6 (x-y)+9+(x-y) 2+25+10 (x-y) = 2 (x-y) 2+4 (x-y)+36 = 0.

(x-y)2+2(x-y)+ 18=0

There is something wrong with this question, please check it carefully!

2.c

Step 4 fill in the blanks

1. If x+y=- 1 and x-y=-3, then x? -Really? =_3_____.

2. If the result of calculating (a+m)(a+ 1/2) does not contain the first item about the letter A, then m= equals _ _- 1/2 _ _.

3. When x=3 and y= 1, the algebraic expression (x+y)(x-y)+y? The value of is _ 9 _ _ _ _ _.

Verbs (short for verb) solve problems.

1. Try to explain that the square difference between two adjacent positive integers is odd.

Solution: (k+1) 2-k2 = k2+1+2k-k2 = 2k+1.

odd number

2. Calculation: (2+ 1)×(2? + 1)×(2^4+ 1)×…×(2^2n+ 1)

(2- 1)(2+ 1)×(2? + 1)×(2^4+ 1)×…×(2^2n+ 1)=2^(2n+ 1)- 1