Math, asked by atheena, 1 year ago

factorise (p-q)³+(q-r)³+(r-p)³

thinkdifferent: If a+b+c =0 then a3+b3+c3 = 3abc in this question let a= (p-q) ,b= (q-r) , c= (r-p) than a+b+c = p - q + q- r + r- p = 0 so
(p-q)3 + ( q-r)3+ (r-p)3 = 3 (p-q)(q-r)(r-p)

This is the shortest way to do these type of questions .................................................................................................................................

Answers

Answered by mysticd

334

Hi ,

*******************************************

If x + y + z = 0 ,

Then ,

x³ + y³ + z³ = 3xyz

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Here ,

Let x = p - q ,

y = q - r ,

z = r - p ;

Now ,

x + y + z = p - q + q - r + r - p

x + y + z = 0

Therefore ,

x³ + y³ + z³ = 3xyz

( p - q )³ + ( q - r )³ + ( r - p )³

= 3( p - q )( q - r )( r - p )

I hope this helps you.

: )

Answered by Anonymous

166

Hi,

Please see the attached file!

Thanks

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