Question

Find the value of (25a² + 16b² + 9 + 40ab – 24b – 30a) at a = – 1 and b = 2.

Answer 1

Using the identity

(a+b+c)2 = a² + b² + c² + 2ab + 2bc + 2ca

25a² + 16b² + 9 + 40ab -24b -30a

= (5a)² + (4b)² + (-3)² +2 x 5a x 4b + 2 x 4b x (-3) + 2 x 5a x (-3)

= (5a + 4b -3)²

∴ Required value = (5 x (-1) + 4 x 2 -3)²

= (-5 + 8 - 3)² = (-8 + 8)² = 0.