(i) -5y2 from y2
= y2 – (-5y2)
= y2 + 5y2 = 6y2
(ii) 6xy from – 12xy
= -12xy – (6xy)
= -12xy – 6xy = -18xy
(iii) (a – b) from (a + b)
= a + b – (a – b)
= a + b - a + b
= 2b
(iv) a(b – 5) from b(5 – a)
= ab – 5a from 5b – ab
= (5b – ab) – (ab – 5a)
= 5b – ab – ab + 5a
= 5a – 5b – 2ab
(v) -m2 + 5mn from 4m2 – 3mn + 8
= (4m2 – 3mn + 8) – (-m2 + 5mn)
= 4m2 – 3mn + 8 + m2 – 5mn
= 4m2 + m2 – 3mn – 5mn + 8
= 5m2 – 8mn + 8
(vi) -x2 + 10x – 5 from 5x – 10
= (5x – 10) – (-x2 + 10x – 5)
= 5x – 10 + x2 – 10x + 5
= 5x – 10x + x2 – 10 + 5
= x2 – 5x – 5
(vii) 5a2 – 7 ab + 5b2 from 3ab – 2a2 – 2b2
= (3ab – 2a2 – 2b2) – (5a2 – 7ab + 5b2)
= 3ab – 2a2 – 2b2 – 5a2 + 7ab – 5b
= -2a2 – 5a2 – 2b2 – 5b2 + 7ab + 3ab
= -7a2 – 7b2 + 10ab
(viii) 4pq – 5q2 – 3p2 from 5p2 + 3q2 – pq
= (5p2 + 3q2 – pq) – (4pq – 5q2 – 3p2)
= 5p2 + 3q2 – pq2 – 4pq + 5q2 + 3p2
= 5p2 + 3p2 + 3q2 + 5q2 – 4pq – pq
= 8p2 + 8q2 – 5pq
