Solve simultaneous linear equations: (i) (x2 – y2)z + (y2 – z2)x

Solve simultaneous linear equations:

(i) (x² – y²)z + (y² – z²)x
(ii) 5a⁴ – 5a³ + 30a² – 30a

Solution:

(i) (x² – y²)z + (y² – z²)x
Above terms can be written as,
zx² – zy² + xy² – xz²
Rearrange the above terms we get,
zx² – xz² + xy² – zy²
Take out common in both terms,
zx(x – z) + y²(x – z)
(x – z) (zx + y²)
(ii) 5a⁴ – 5a³ + 30a² – 30a
5a⁴ – 5a³ + 30a² – 30a
Take out common in both terms,
5a(a³ – a² + 6a – 6)
5a[a²(a – 1) + 6(a – 1)]
5a(a – 1) (a² + 6)

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