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Mathematics

Factorise the following:

x(x2 + y2 - z2) + y(-x2 - y2 + z2) - z(x2 + y2 - z2).

Factorisation

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Answer

The above expression:

x(x2 + y2 - z2) + y(-x2 - y2 + z2) - z(x2 + y2 - z2)

can be written as

x(x2 + y2 - z2) + y(-1)(x2 + y2 - z2) - z(x2 + y2 - z2)
= x(x2 + y2 - z2) - y(x2 + y2 - z2) - z(x2 + y2 - z2).

H.C.F. of x(x2 + y2 - z2), y(x2 + y2 - z2) and z(x2 + y2 - z2) is (x2 + y2 - z2).

∴ x(x2 + y2 - z2) + y(-x2 - y2 + z2) - z(x2 + y2 - z2) = (x2 + y2 - z2)(x - y - z).

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