Help me to do some multiplication formula application 1. Calculate the second power of 3000 - the second power of 2999 + the second power of 2998 - the second power of 2997 +. + the second power of 4 - the second power of 3 + the first power of 2 - the second power of 1 2. It is known that a.b.c.d are all positive numbers, and the fourth power of a + the fourth power of B + the fourth power of C + the fourth power of D = 4abcd. It is proved that a = b = C = D | Math enthusiast | Mathematical art

Help me to do some multiplication formula application 1. Calculate the second power of 3000 - the second power of 2999 + the second power of 2998 - the second power of 2997 +. + the second power of 4 - the second power of 3 + the first power of 2 - the second power of 1 2. It is known that a.b.c.d are all positive numbers, and the fourth power of a + the fourth power of B + the fourth power of C + the fourth power of D = 4abcd. It is proved that a = b = C = D

Question 1: use the square difference formula 3000 ^ 2-2999 ^ 2 + 2998 ^ 2-2997 ^ 2 +. + 4 ^ 2-3 ^ 2 + 2 ^ 2-1 = (3000 + 2999) * (3000-2999) + (2998 + 2997) * (2998-2997) +... + (2 + 1) * (2-1) = 3000 + 2999 + 2998 + 2997 +... + 2 + 1 = 3000 * 3001 / 2 = 4501500

5 + 10 + 15 + 20 + 25

5+2×5+3×5+4×5+5×5=5(1+2+3+4+5)=75

5 + 10 + 15 + 20 + 25 change multiplication formula 2 + 4 + 6 + 8 + 10 + 12 change multiplication formula

5＋10＋15＋20＋25
=15×5
=75
2＋4＋6＋8＋10＋12
=(2+12)+(4+10)+(6+8)
=3×14
=42

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