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)#