i. (2p + q + 5)2
= (2p)2 + (q)2 + (5)2 + 2(2p) (q) + 2(q) (5) + 2(2p) (5) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac]
= 4p2 + q2 + 25 + 4pq + 10q + 20p
ii. (m + 2n + 3r)2
= (m)2 + (2n)2 + (3r)2 + 2(m) (2n) + 2(2n) (3r) + 2(m) (3r) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac]
= m2 + 4n2 + 9r2 + 4mn + 12nr + 6mr
iii. (3x + 4y – 5p)2
= (3x)2 + (4y)2 + (- 5p)2 + 2(3x) (4y) + 2(4y) (- 5p) + 2(3x) (- 5p) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac]
= 9x + 16y2 + 25p2 + 24xy – 40py – 30px
iv. (7m – 3n – 4k)2
= (7m)2 + (- 3n)2 + (- 4k)2 + 2(7m) (- 3n) + 2 (- 3n) (- 4k) + 2 (7m) (- 4k) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac]
= 49m2 + 9n2 + 16k2 – 42mn + 24nk – 56km
