Question

factorise
xy^2-yx^2-xy+z^2​

Answer 1

Answer:

(x-y) (y-z) (z-x)

Step-by-step explanation:

x(y²−z²)+y(z²−x² )+z(x² −y²)

=xy 2−xz² +yz²−yx² +zx² −zy²

Arrange the terms in descending order of power of x.

=−x² y+zx² +xy²−xz² −yz +yz² =−x² (y−z)+x(y²−z² )−yz(y−z)

=−x² (y−z)+x(y−z)(y+z)−yz(y−z)

=(y−z)[−x² +x(y+z)−yz](y−z)[−x²+xy+xz−yz]

Arrange the term in bracket in descending order of the power of y.

=(y−z)[xy−yz−x

2

+xz]

=(y−z)[−y(−x+z)+x(−x+z)]

=(x−y)(y−z)(z−x).

I hope it helps you out

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