How do you factor #216g ^ { 3} - 125u ^ { 6}#?

1 Answer
George C.
Jul 16, 2017

#216g^3-125u^6 = (6g-5u^2)(36g^2+30gu^2+25u^4)#

Explanation:

The difference of cubes identity can be written:

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

We can use this with #a=6g# and #b=5u^2# to find:

#216g^3-125u^6 = (6g)^3-(5u^2)^3#

#color(white)(216g^3-125u^6) = (6g-5u^2)((6g)^2+(6g)(5u^2)+(5u^2)^2)#

#color(white)(216g^3-125u^6) = (6g-5u^2)(36g^2+30gu^2+25u^4)#

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