If x-y=3, then what is x^{3}-y^{3}-9xy?

Sarah-Louise Prince

Sarah-Louise Prince

Answered question

2022-02-28

If xy=3, then what is x3y39xy?

Answer & Explanation

star233

star233

Skilled2022-03-10Added 403 answers

Step 1Simply cube the equationSo(xy)3=x3y33xy(xy)=33=27But we know xy=3 So substituting in the equationSox3y33xy(3)=x3y39xy=27
alenahelenash

alenahelenash

Expert2022-03-10Added 556 answers

Step 1x3y3=(xy)×(x2+xy+y2)xy=3, then (xy)2=9, thus x2xy+y2=9x2+xy+y2=x22xy+y2+3xy, sox2+xy+y2=9+3xyBack to our question: we have now the value of xy and x2+xy+y2.(xy)×(x2+xy+y2)9xy=3×(9+3xy)9xy=27+9xy9xy=27

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