Question

Show that (x+y)^3=x^3+y^3+3xy(x-y)​

Answer 1

Answer:

(x+y)³=x³+y³+3xy(x+y)

(x+y)³=

(x+y)(x+y)(x+y)

(x+y)²(x+y)

= (x²+y²+2xy) (x+y)

= x(x²+y²+2xy) +y(x²+y²+2xy)

= x³+xy²+2x²y+x²y+y³+2xy²

= x³+ 3xy²+y³+3x²y

= x³+y³+3xy(x+y)

therefore RHS= LHS

Answer 2

Step-by-step explanation:

(x+y)^3

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

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

=>[x^2+xy+xy+y^2](x+y)

=>x (x^2+2xy+y^2)+y (x^2+2xy+y^2)

=>x^3+2x^2y+xy^2+x^2y+2xy^2 +y^3

=>x^3+y^3+3x^2y+3xy^2

=>x^3+y^3+(3x^2y+3xy^2)

=>x^3+y^3+3xy (x+y)