Simplify the following (2x + 3y + 4z)

(2x + 3y + 4z) (4x² + 9y² + 16z² – 6xy – 12yz – 8zx).

Answer :

(2x + 3y + 4z) (4x² + 9y² + 16z² – 6xy – 12yz – 8zx)

It can be written as

= (2x + 3y + 4z) ((2x)² + (3y)² + (4z)² – 2x × 3y – 3y × 4z – 4z × 2x)

By further calculation

= (2x)³ + (3y)³ + (4z)³ – 3 × 2x × 3y × 4z

So we get

= 8x³ + 27y³ + 64z³ – 72xyz

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