( 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