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Factorise
(i) 2x
2
(x + y) - 3(x + y)
(ii) 5xy(5x + y) - 5y(5x + y)
(iii) x(x
2
+ y
2
- z
2
) + y(x
2
+ y
2
- z
2
) + z(x
2
+ y
2
- z
2
)
(iv) ab(a
2
+ b
2
- c
2
) + bc(a
2
+ b
2
- c
2
) + ca(a
2
+b
2
-c
2
)
(i) 2x
2
(x + y) - 3(x + y)
= (x + y) (2x
2
- 3)
(ii) 5xy(5x + y) - 5y(5x + y)
= 5y(5x + y) (x - 1)
(iii) x(x
2
+ y
2
- z
2
) + y(x
2
+ y
2
- z
2
) + z(x
2
+ y
2
- z
2
)
= (x
2
+ y
2
- z
2
) (x + y + z)
(iv) ab(a
2
+ b
2
- c
2
) + bc(a
2
+b
2
-c
2
) + ca(a
2
+b
2
- c
2
)
= (a
2
+ b
2
- c
2
) (ab + bc + ca)
9
