Question

The product of two numbers is ( x⁶-y⁶).if one of the numbers is (x-y) then find the other​

Answer 1

AnswEr:-

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: -

Let the required number be z.

Now,

=>  x^6 - y^6 =  (x³)² - (y³)²

• [a² - b² = (a-b)(a+b)]

 =>   ( x³ - y³)(x³ + y³)

• a³ - b³ = (a-b)(a²+ab+b²)

    => (x - y)(x² + xy + y²)(x³ + y³)

Now ,

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

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

Hence, the required number is   z = (x² + xy + y²)(x³ + y³).

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Answer 2

x^6-y^6= (x^3)^2 -(y^3)^2= (x^3-y^3) (x^3+y^3)

x^3-y^3= (x-y)^3 -3xy(x-y)

x^3-y^3= (x-y)[ (x-y)^2-3xy]

x^3-y^3=(x-y)[x2-5xy+y^2]

so x^6-y^6 = (x-y) [x^2-5xy+y^2] [x^3+y^3]

so

x^6-y^6/(x-y) = (x-y) [x^2-5xy+y^2] [x^3+y^3]/(x-y)

x^6-y^6/(x-y) =[x^2-5xy+y^2] [x^3+y^3]