Factorise each of the following expression:
(i) $a^{3} x + a^{2} (x - y) - a (y + z) - z$
(ii) $(x^{2} + 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y$ .

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Solution

(i) We have,
$a^{3} x + a^{2} (x - y) - a (y + z) - z$
$= a^{3} x + a^{2} x - a^{2} y - a y - a z - z$
$= (a^{3} x + a^{2} x) - (a^{2} y + a y) - (a z + z)$
$= a^{2} x (a + 1) - a y (a + 1) - z (a + 1)$
$= (a + 1) (a^{2} x - a y - z)$

(ii) We have
$(x^{2} + 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y$
$= (x^{2} + 3 x) {(x^{2} + 3 x) - 5} - y {(x^{2} + 3 x) - 5} = (x^{2} + 3 x - 5) (x^{2} + 3 x - y$

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Similar questions

(i) a^{3} x + a^{2} (x - y) - a (y + z) - z

(i i) (x^{2} + 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y

(x^{2} + 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y

(x^{2} - 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y

= (x^{2} + 3 x - 5) (x^{2} + 3 x - y)

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