Expand
(i) (x + 5y + 6z)2
(ii) (2a - 3b + 4c)2
(iii) (-a + 6b + 5c)2                 
(iv) (-p +4q - 3r)2
Using the identity
(x + y + z)2 = x2 + y2 + 2xy + 2yz + 2xz, we have
(i) (x + 5y + 6z)2    
= (x)2 + (5y)2 + (6z)2 + 2(x)(5y) + 2(5y)(6z) + 2(x)(6z)
= x2 + 25y2 + 36z2 + 10xy + 60yz + 12 xz
(ii) (2a - 3b + 4c)2
= (2a)2+(-3b)2+(4c)2+2(2a)(-3b)+2(-3b)(4c)+2(2a)(4c)
= 4a2+ 9b2 + 16c2 - 12ab - 24bc + 16ac
(iii) (-a + 6b + 5c)2
= (-a)2+(6b)2+(5c)2+2(-a)(6b)+2(6b)(5c)+2(-a)(5c)
= a2 + 36b2 + 25c2 - 12ab + 60bc - 10ac
(iv) (-p + 4q - 3r)2
= (-p)2+(4q)2+(-3r)2+2(-p)(4q)+2(4q)(-3r)+2(-p)(-3r)
= p2 + 16q2 + 9r2 - 8pq - 24qr + 6pr
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