(x+y+z)^3 x^3 y^3 z^3

Standard VIII

Mathematics

Factorisation by Grouping Terms

We know the identity: (a+b+c)3−a3−b3−c3=3(a+b)(b+c)(c+a)

Using the above identity taking a=x, b=−y and c=−z, the equation (x−y−z)3−x3+y3+z3 can be factorised as follows:

(x−y−z)3−x3+y3+z3=3(x−y)(−y−z)(−z+x)=−3(x−y)(y+z)(−z+x)=3(x−y)(y+z)(z−x)

Hence, (x−y−z)3−x3+y3+z3=3(x−y)(y+z)(z−x)

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