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1.
(1+5)(1^2-(1*5)+5^2)= 126: Sum of cubes 1^3+ 5^3

2.
(1/a)+(1/b)= (a+b)/ab: Sum of reciprocals

3.
(2+3)(2^2-(2*3)+3^2)= 35: Sum of cubes 2^3+3^3

4.
(2+3)/(2*3)= 5/6: sum of reciprocals 1/2 + 1/3

5.
(4+5)/(4*5)= 9/20: sum of reciprocals 1/4 + 1/5

6.
(4-3)(4^2+(4*3)+3^2)= 37: Difference of cubes 4^3-3^3

7.
(5+7)/(5*7)= 12/35: sum of reciprocals 1/5 + 1/7

8.
(5-4)(5^2+(5*4)+4^2)= 61: Difference of cubes 5^3-4^3

9.
x^2+y^2= (x+y)^2-2xy: Sum of Squares

10.
x^2-y^2= (x+y)(x-y): Difference of Squares

11.
x^3+y^3=(x+y)(x^2-xy+y^2): Sum of Cubes

12.
x^3-y^3= (x-y)(x^2+xy+y^2): Difference of Cubes

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