How do you simplify (p^3-1)/(5-10p+5p^2)p3−15−10p+5p2?

1 Answer
Shwetank Mauria
Jan 24, 2017

(p^3-1)/(5-10p+5p^2)=(p^2+p+1)/(5(p-1))p3−15−10p+5p2=p2+p+15(p−1) or (p^2+p+1)/(5p-5)p2+p+15p−5

Explanation:

To simplify (p^3-1)/(5-10p+5p^2)p3−15−10p+5p2, we should first factorize numerator and denomiantor.

p^3-1=p^3-p^2+p^2-p+p-1p3−1=p3−p2+p2−p+p−1

= p^2(p-1)+p(p-1)+1(p-1)p2(p−1)+p(p−1)+1(p−1)

= (p^2+p+1)(p-1)(p2+p+1)(p−1)

and 5-10+5p^2=5(p^2-2p+1)5−10+5p2=5(p2−2p+1)

= 5(p^2-p-p+1)=5(p(p-1)-1(p-1))=5(p-1)(p-1)5(p2−p−p+1)=5(p(p−1)−1(p−1))=5(p−1)(p−1)

Hence (p^3-1)/(5-10p+5p^2)p3−15−10p+5p2

= ((p^2+p+1)(p-1))/(5(p-1)(p-1))(p2+p+1)(p−1)5(p−1)(p−1)

= ((p^2+p+1)cancel((p-1)))/(5(p-1)cancel((p-1)))

= (p^2+p+1)/(5(p-1)) or (p^2+p+1)/(5p-5)

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