Calculation: 2009 power of 2 + 2008 power of 2 = 2007 power of 2 +... + 2 + 1 (1) Observe the following patterns: （a-1)(a+1)=a²-1, （a-1)(a²+a+1)=a³-1 (A-1) (a 3 + a 2 + A + 1) = the fourth power of A-1, ...... According to the above formula, please write: Calculation: 2009 power of 2 + 2008 power of 2 = 2007 power of 2 +... + 2 + 1 (2) A community has a rectangular green space, and now it is planned into a square green space. If the width is increased by two meters and the length is reduced by two meters, the area can be tripled. What is the original area of this green?

2's 2009 power + 2's 2008 power + 2's 2007 power +... + 2 + 1
In fact, it is the sum of equal proportion sequence. A1 = 1, q = 2, n = 2010, Sn = A1 (1-Q ^ n) / (1-Q)
=2^2010-1.
According to the supplement, let a = 2, the result of the formula is obviously 2 ^ 2010-1
(2) The length and width of the rectangular green space are a and B. now, it is planned to be a square green space. If the width is increased by two meters and the length is reduced by two meters, the area of the square green space can be expanded three times,
a-2=b+2 (1) ->a-b=4
(a-2)*(b+2)=3ab (2) ->ab+2a-2b-4=3ab ->2(a-b)-4=2ab (3)
2*4-4=2ab ->ab=2

What is the 2009 power of 2 minus the 2008 power of 2

2^2009*-2^2008
=(2^2008)*2-2^2008
=2^2008*(2-1)
=2^2008.

5 to the 2009 power - 7 × 5 to the 2008 power + 10 × 5 to the 2007 power, 5 to the 2009 power - 7 × 5 to the 2008 power + 10 × 5 to the 2007 power

=5^2007(5^2-7x5+10) =5^2007(25-35+10) =0

What is the 2009 power of 8 minus the 2008 power of 8

2008 power of 8 = 2008 power of 8 * 2008 power of 8 = 2008 power of 8 * 2008 power of 8 = 2008 power of 8 * (8-1) = 2008 power of 8 * 7

Calculation: (- 2) 2008 power + (- 2) 2009 power is equal to

(-2)^2008+(-2)^2009 =2^2008+(-2)*2^2008 =2^2008-2*2^2008 =-2^2008

How much is the 2008 power of - 2 plus the 2009 power of - 2? But I don't know how.

(-2)^2008 +(-2)^2009
=(-2)^2007 * (-2) + (-2)^2007 *(-2)^2
=(-2)^2007 * [(-2)+(-2)^2]
=-2^2007 * 2^1
= - 2^2008

Simple calculation: the 2nd power of 2009 - 2008 × 2010

2009²-2008×2010
=2009²-(2009-1)(2009+1)
=2009²-(2009²-1)
=2009²-2009²+1
=1

Calculate 2's 2009 power - 2's 2008 power is equal to A. 2's 2008 B. 2 C. 1'd - 2's 2009 process. Thank you Come on, thank you

The 2009 power of 2 is equal to the 2008 power of 2 * 2, and the two are subtracted to extract the 2008 power of common factor 2 = the 2008 power of 2

Calculation: the 2009 power of (- 2) plus the 2008 power of 2 is equal to?

(-2)^2009+2^2008
=2^2008-2^2009
=2^2008(1-2)
=-2^2008

2's 2009 power - 5 * 2's 2008 power + 6 * 2's 2007 power + 2010 factorization

2^2009-5×2^2008+6×2^2007+2010
　　=4×2^2007-10×2^2007+6×2^2007+2010
　　=(4-10+6)×2^2007+2010
　　=0×2^2007+2010
　　=2010