Which one of the following is one of the factors of x2 (y – z) + y2 (z – x) – z (xy – yz – zx)?

Given: x2 (y – z) + y2 (z – x) – z(xy – yz – zx)= x2y – x2z + y2z – y2x – zxy + yz2 + z2x= xy(x – y – z) + z2(x + y) – z (x2 – y2)= xy(x – y – z) – z (x + y) (x – y – z) = (x – y – z) (xy – yz – zx)

Which one of the following is one of the factors of x2 (y – z) + y2 (z – x) – z (xy – yz – zx)?

Given: x2 (y – z) + y2 (z – x) – z(xy – yz – zx)= x2y – x2z + y2z – y2x – zxy + yz2 + z2x= xy(x – y – z) + z2(x + y) – z (x2 – y2)= xy(x – y – z) – z (x + y) (x – y – z) = (x – y – z) (xy – yz – zx)

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Which one of the following is one of the factors of x² (y – z) + y² (z – x) – z (xy – yz – zx)?

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(x - y - z)(xy - yz - zx)

(y – z) (x – yz – z)

(xz – yx – z) (x – yz – zx)

(yx – y – z) (z – yz – xz)

answer is A.

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Detailed Solution

Given: x² (y – z) + y² (z – x) – z(xy – yz – zx)
= x²y – x²z + y²z – y²x – zxy + yz² + z²x
= xy(x – y – z) + z²(x + y) – z (x² – y²)
= xy(x – y – z) – z (x + y) (x – y – z)