How do you simplify #(16x^3 - 2y^3)/(16x^3 + 8x^2 y + 4xy^2)#?

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Answer 1 · 2018-03-02T05:14:47

#= (2x-y)/(2x)#

You can only cancel if you have factors.

Factorise top and bottom first by taking out the common factor.

#(16x^3-2y^3)/(16x^3 +8x^2y+4xy^2) = (2(8x^3-y^3))/(4x(4x^2+2xy+y^2)#

THe numerator can be factored further as the difference of cubes:

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

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

Now cancel the factors which are the same.

# = (cancel2(2x-y)cancel((4x^2+2xy+y^2)))/(cancel4^2xcancel((4x^2+2xy+y^2))#

#= (2x-y)/(2x)#

Recall: Difference of cubes:

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