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How do you factor #2a^3-16#?

1 Answer

May 16, 2015

The factor 2 is common to both the terms in the expression

#2a^3-16 = 2(a^3 - 8)#

# = 2(a^3 - 2^3)#

We know that #color(blue)(x^3 - y^3 = (x-y)(x^2 + xy +y^2)#
( Difference of Cubes Identity )

Hence #2(a^3 - 2^3) = 2(a-2)(a^2+2a+2^2)#

# = color(green)(2(a-2)(a^2+2a+4)#

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