How do you factor #8x^3+y^3#?

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Answer 1 · 2017-04-02T05:50:11

#8x^3+y^3=(2x+y)(4x^2-2xy+y^2)#

#8x^3+y^3# is a sum of two cubes as it is equivalent to #(2x)^3+y^3#

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

Hence, #8x^3+y^3=(2x)^3+y^3#

= #(2x+y)((2x)^2-(2x)y+y^2)#

= #(2x+y)(4x^2-2xy+y^2)#

Alternatively, #8x^3+y^3#

= #8x^3+color(red)(4x^2y-4x^2y)color(blue)(-2xy^2+2xy^2)+y^3#

= #4x^2(2x+y)-2xy(2x+y)+y^2(2x+y)#

= #(2x+y)(4x^2-2xy+y^2)#