Question

find the product using suitable identity (x + Y + 2z)(x2 + y2 + 4z2 - xy - 2yz - 2zx)
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Answer 1

Answer: (x³ + y³ + 8z³) - 6xyz

Step-by-step explanation:

We know,

(a³ + b³ + c³) - 3abc = (a + b + c) × (a² + b² + c² - ab - bc - ca)

Therefore, conventionally

(x + y + 2z) × [x² + y² + (2z)² - xy - y2z - 2zx]          (this is similar to the property)

Thus we converge it in a similar form of (a³ + b³ + c³) - 3abc, i.e.,

[x³ + y³ + (2z)³] - 3xy2z

=> (x³ + y³ + 8z³) - 6xyz