Question

prove that (x + y)^3= x^3 + y^3 + 3 xy ( x + y )​ natural numbers​

Answer 1

To prove :

(x + y)³ = x³ + y³ + 3 xy ( x + y )​

Step-by-step explanation:

=> (x + y)³ = (x + y) (x + y) (x + y)

               

                = [ (x + y) (x + y) ] (x + y)

                = [ x(x + y) + y(x + y) ] (x + y)

                = [ x(x) + x(y) + y(x) + y(y) ] (x + y)

                = [ x² + xy + xy + y² ] (x + y)

                = [ x² + 2xy + y² ] (x + y)

                = x² (x + y) + 2xy(x + y) + y²(x + y)

                = x²(x) + x²(y) + 2xy(x) + 2xy(y) + y²(x) + y²(y)

                = x³ + x²y + 2x²y + 2xy² + xy² + y³

                = x³ + y³ + x²y + 2x²y + 2xy² + xy²

                = x³ + y³ + 3x²y + 3xy²

                = x³ + y³ + 3xy(x) + 3xy(y)

                = x³ + y³ + 3xy(x + y)

_______________________________

Some of the standard algebraic identities are :  

• (a + b)² = a² + 2ab + b²

• (a – b)² = a² – 2ab + b²

• a² – b² = (a + b)(a – b)

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

• (a + b)³ = a³ + b³ + 3ab (a + b)

• (a – b)³ = a³ – b³ – 3ab (a – b)

Answer 2

Step-by-step explanation:

Please kindly refer the attachment................