Question

Find the following products

( 1 ) ( x + y+ 2z ) ( x² + y² + 4z² -xy - 2yz -2zx )


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Answer 1

→ Hey Mate,

→ Given Question:-

→ Find the product of ⇒

→  ( x + y+ 2z ) ( x² + y² + 4z² -xy - 2yz -2zx )

→ Identity used :-

→ ( a + b + c ) ( a² + b² + c² -ab -bc -ca)

→ Solution:-

→ We have,

→  ( x + y+ 2z ) ( x² + y² + 4z² -xy - 2yz -2zx )

→  ( x + y + 2z ) ( x² + y² + (2z)² - x × y - y × 2z -2z × x)

→ ( a + b + c ) ( a² + b² + c² -ab -bc -ca)

→ where,  a = x ,

→                b = y ,

→                c = 2z

→ a³ + b³ + c³ - 3abc

→ x³ + y³ + (2z)³ -3 × x × y × 2z

→ x³ + y³ + 8z³ - 6xyz

→ Hence ,the final answer is  x³ + y³ + 8z³ - 6xyz.

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