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Find the product (2a + 3b – 4c) (4a2 + 9b2 + 16c2 – 6ab + 12bc + 8ca).

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Best answer

Use the identity

(x + y + z) (x2 + y2+ z2– xy – yz – zx) = x3 + y3 + z3 – 3xyz

Here, x = 2a, y = 3b and z = – 4c

∴ (2a + 3b - 4c)(4a2 +9b2 + 16c2 - 6ab + 12bc + 8ca)

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

= 8a3 + 27b3 - 64c3 + 72abc.

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