How do you factor #216a^3b^3-343c^6#?

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Answer 1 · 2018-07-06T11:36:36

#color(blue)((6ab-7c^2)(36a^2b^2+42abc^2+49c^4)#

First notice:

#216=6^3#

and:

#343=7^3#

We can now write:

#6^3a^3b^3-7^3c^6#

Which leads to:

#(6ab)^3-(7c^2)^3#

This is the difference of two cubes:

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

#:.#

#(6ab-7c^2)(36a^2b^2+42abc^2+49c^4)#

Answer 2 · 2018-07-06T11:46:30

#(6ab-7c^2)(36a^2b^2+42abc^2+49c^4)#

Note that

#216a^3b^3=(2*3*a*b)^3#
and

#343c^6=(7c^2)^2#

we use the formula

#a^3-b^3=(a-b)(a^2+ab+b^2)#
so we get

#(6ab-7c^2)(36a^2b^2+42abc^2+49c^4)#