Question

the product of two numbers x6 - y6 if one of the numbers is x-y then find the other number

Answer 1

Given: the product of two numbers x^6 - y^6.

To find: if one of the numbers is x-y then find the other number

Solution:

• Now we have given that the one of the numbers is x-y .

• Let the other number be z.

• Now x^6 - y^6 can be written as:

                    (x³)² - (y³)²

• Now according to the formula a² - b² = (a-b)(a+b), we get:

                    ( x³ - y³)(x³ + y³)

• Now according to the formula a³ - b³ = (a-b)(a²+ab+b²), we get:

                    (x - y)(x² + xy + y²)(x³ + y³)

• Now according to the question, we have:

                    z × (x - y) = (x - y)(x² + xy + y²)(x³ + y³)

                    z = (x² + xy + y²)(x³ + y³)

Answer:

          So the other number is (x² + xy + y²)(x³ + y³).

Answer 2

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