1729 is the smallest number that can be expressed in two ways as the sum of two cubes.[12cube+9cube] * * * * * ... two positive cubes. 12 cube + 1 cube and 10 cube + 9 cube.
a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2
(a3 + b3) = (a + b)(a2 - ab + b2)
(xy + 7)(x^2y^2 - 7xy + 49)
Do in this order. 1. All, find the gfc 2. Binomial, factor as difference of squares, sum of cubes, difference of cubes. 3. Trinomial, factor as a quadratic. 4. 4 or more terms, factor by grouping.
The sum of two cubes can be factored as below.a3 + b3 = (a + b)(a2 - ab + b2)
a3 + b3
That means that you calculate the cubes of two numbers, and then either add or subtract them.
1
The sum of their squares is 10.
1
50%
Sum and difference of two cubes is factored this way : a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
You get the sum of 11 two ways; 5,6 and 6,5.
23 = 8, 33 = 27. Sum 35, difference 19...
According to Ramanujan, it's the lowest number that can be expressed in two different ways as the sum of two cubes (the cubes of 12 and 1; the cubes of 10 and 9). It 's the answer.
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