How do you simplify #(2x^3-32x)/(x^2+8x+16)#?

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Answer 1 · 2018-03-28T20:02:09

See below

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

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Answer 2 · 2018-03-28T20:04:37

#=(2x(x-4))/((x+4))#

You cannot cancel despite it being so tempting to do so.
There are #+ and -# signs which prevent it!!

Factorise first.

#(2x^3-32x)/(x^2+8x+16)" "(larr"common factor")/(larr"quadratic trinomial")#

#=(2x(x^2-16))/((x+4)(x+4))" "(larr"difference of squares")/(larr"two factors")#

#=(2xcancel((x+4))(x-4))/(cancel((x+4))(x+4))" "larr# cancel common factors

#=(2x(x-4))/((x+4))#