How do you simplify $(7x-1)(49x^2+7x+1)(343x^3+1)$ ?

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Answer 1 · 2015-06-14T20:25:16

$(7x-1)(49x^2+7x+1)(343x^3+1) = (7x)^6-1$

$(7x)^6-1$

$= ((7x)^3)^2-1^2$

$= ((7x)^3-1)((7x)^3+1)$

$= ((7x)^3-1^3)((7x)^3+1)$

$= (7x-1)((7x)^2+7x+1)((7x)^3+1)$

$= (7x-1)(49x^2+7x+1)(343x^3+1)$

using the difference of square identity:

$a^2-b^2 = (a-b)(a+b)$

and the difference of cubes identity:

$a^3-b^3 = (a-b)(a^2+ab+b^2)$

How do you simplify (7x-1)(49x^2+7x+1)(343x^3+1)(7x-1)(49x^2+7x+1)(343x^3+1)?