The sum of 3 consecutive integers in 132

Here we will use algebra to find three consecutive integers whose sum is 132. We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 132. Therefore, you can write the equation as follows: X + X + 1 + X + 2 = 132.

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answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb