anonymous
  • anonymous
solve this :
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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Jhannybean
  • Jhannybean
http://www.lightshot.skillbrains.com For your screenshots :)
Callisto
  • Callisto
\[\frac{(x-y)(x^4-y^4)}{x^3+xy^2+x^2y+y^3}\]Factorize the numerator and denominator.\[=\frac{(x-y)^2(x+y)(x^2+y^2)}{x^2(x+y)+y^2(x+y)}\]\[=\frac{(x-y)^2(x+y)(x^2+y^2)}{(x^2+y^2)(x+y)}\]I think you know the rest.

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Jhannybean
  • Jhannybean
@Callisto how did you factorize the numerator? :o
Jhannybean
  • Jhannybean
Oh wait....a minute...it'd be..
Jhannybean
  • Jhannybean
(x-y)(x^2-y^2)(x^2+y^2) right? haha.
anonymous
  • anonymous
We have : \[(x^4-y^4)=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)=4(x^3+xy^2+yx^2+y^3)\] hence : \[\frac{(x-y)(x^4-y^4)}{x^3+xy^2+yx^2+y^3}=\frac{(x-y)\times\left(4(x^3+xy^2+yx^2+y^3)\right)}{x^3+xy^2+yx^2+y^3}=4^2=16\]
Callisto
  • Callisto
And\[(x-y)(x^2-y^2)(x^2+y^2)\]\[=(x-y)(x+y)(x-y)(x^2+y^2)\]\[=(x-y)^2(x+y)(x^2+y^2)\]
Jhannybean
  • Jhannybean
Gotcha. This happens when you're up at 3 am doing math xD
anonymous
  • anonymous
@Jhannybean i cannot open that link :( @Callisto and @Noura11 thanks both of you :)

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