How do you factor #4a^3-64a#?

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Answer 1 · 2016-05-07T20:47:14

#4a(a-4)(a+4)#

4 is a factor of both 4 and 64

#a# is a factor of both #4a^2" and "64a#

Factor out #4a# giving:

#4a(a^2-16)#

But 16 is the same as #4^2#

#4a(a^2-4^2)#

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compare to the example #y^2-z^2=(y-z)(y+z)#
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#color(brown)(4a(a^2-4^2))color(blue)(" "->" "4a(a-4)(a+4)#