Expand: (3a + 4b + 5c)2.
We have,
(3a + 4b + 5c)2
We know that,
(a + b + c)2 = a2 + y2 + c2 + 2 (xy + yz + zx)
∴ (3a + 4b + 5c)2 = (9a2 + 16b2 + 25c2 + 2 × 3a × 4b + 2 × 4b × 5c + 2 × 5c × 3a)
= 9a2 + 16b2 + 25c2 + 24ab + 40bc + 30ac