For two integers a and B, a * b = (a + b) * a, a + B = a * B + 1, find [(- 2) * - 5)] + (- 4)

For two integers a and B, a * b = (a + b) * a, a + B = a * B + 1, find [(- 2) * - 5)] + (- 4)

From the relation of a * b = (a + b) * a, we know that (- 2) * (- 5) = [(- 2) + (- 5)] * (- 2) = 14
So [(- 2) * (- 5)] + (- 4) = 14 + (- 4)
From a + B = a * B + 1, we know that 14 + (- 4) = 14 * (- 4) + 1 = - 55
So [(- 2) * (- 5)] + (- 4) = - 55

For two integers a and B, a × B = (a + b) a, a + B = AB + 1, find the value of [(- 2) × (- 5)] + (- 4)

【（-2）×（-5）】+（-4）
=[-7×(-2)]+(-4)
=14+(-4)
=14×(-4)+1
=-56+1
=-55

For two integers a and B, a * b = (a + b) a, a ⊕ B = a · B + 1, find [(- 2) * - 5)] ⊕ - 4
For two integers a and B, a * b = (a + b) a, a ⊕ B = a · B + 1, find [(- 2) * - 5)] ⊕ - 4

Just replace it with "*", "♁" are user-defined operation symbols
[（-2）*（-5）]=[（-2）+（-5）](-2)=14
[（-2）*（-5）]♁（-4）=14 ♁（-4）=14·(-4）+1=-55

Try to find the value of - 1 + 2-3 + 4-5 + 6 -... - 2007 + 2008

This problem has two solutions, one is (- 1-3-5 -2007)+(2+4+6… +2008) = (2 + 2008) * 502 - (1 + 2007) * 502 = (2010-2008) * 502 = 2 * 502 = 1004; the second is (2-1) + (4-3) + (6-5) +(2008-2007)=1*1004=1004

Given 1 + A + A ^ 2 + A ^ 3 = 0, find the value of a + A ^ 2 + A ^ 3 + A ^ 4 + A ^ 5 + A ^ 6 + A ^ 7 + A ^ 8 +. + A ^ 2008

a+a^2+a^3+a^4+a^5+a^6+a^7+a^8+.+a^2008
=a(1+a+a^2+a^3)+a^5(1+a+a^2+a^3)+.+a^2005(1+a+a^2+a^3)
=0

Given 2 ^ a · 5 ^ B · 3 ^ C = 6000, where a, B, C are positive integers, find the value of (a-b-c) ^ 2008

2^a·5^b·3^c=6000=2^4*5^3*3^1
So a = 4, B = 3, C = 1
(a-b-c)^2008=(4-3-1)^2008=0

-1 ^ 2009 + (- 5) ^ 2 / | - 5 / 6 | * 2 / 5-4 ^ 2 / (- 2) 3 ② find the value of (a + b) ^ 2008 + A ^ 2009 when | a + 1 | + (b-2) ^ 2 = 0 is known

-1^2009+(-5)^2/|-5/6|*2/5-4^2/(-2)^3
=-1+25×6/5*2/5-16/(-8)
=-1+12+2
=13
② It is known that | a + 1 | + (b-2) ^ 2 = 0
a+1=0 a=-1
b-2=0 b=2
（a+b）^2008+a^2009
=(-1+2)^2008+(-1)^2009
=1-1
=0

If a = 3, B = 1, C = 5, and a + B = a + B, a + C = - (a + C), find the value of A-B + C

3-1 + (- 5) = - 3a, B are positive numbers, C are negative numbers

If | a + 1 | + (b-2) ^ 2 = 0, find the value of (a + b) ^ 2007 + A ^ 2008

|a+1|+(b-2)^2=0,
a+1=0,b-2=0
a=-1,b=2
The power of a + B = 1 is 1
The power of a = - 1 is 1
（a+b）^2007+a^2008=2

(2008-A) (2007-a) = 2003 find the value of (2008-A) ^ 2 - (2007-a) ^ 2

Let 2008-A = x 2007-a = y, then xy = 2003 X-Y = 1 (X-Y) ^ 2 = x ^ 2 + y ^ 2 - 2 XY, so x ^ 2 + y ^ 2 can get 1 + 2003 * 2 = 4007 (x ^ 2 + y ^ 2) ^ 2 = x ^ 4 + y ^ 4 + 2 x ^ 2Y ^ 2 (x ^ 2-y ^ 2) ^ 2 = x ^ 4 + y ^ 4 - 2 x ^ 2Y ^ 2 = x ^ 4 + y ^ 4 + 2 x ^ 2Y ^ 2 = (x ^ 2