Question

prove that
$(x ^{3} + y ^{3} ) = x ^{3} + y ^{3} + 3xy(x + y)$

Answer 1

$\huge \red {Hey \:mate}$

✨ Here's ur answer

to prove

$x ^{3} + y ^{3} ) = x ^{3} + y ^{3} + 3xy(x + y)$

We know that

$x ^{3} + y ^{3}$ . =(x+y) (x+y) (x +y)

=(x+y)
$x ^{2} + 2xy + y ^{2}$
=

$x {}^{3} + 2x ^{2} y + xy ^{2} + yx {}^{2} +2xy ^{2} + y{?}^{3}$

Now,..$x ^{3} + y ^{3} ) = x ^{3} + y ^{3} + 3xy(x + y)$

Answer 2

To prove:

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

Proof:

We know that:

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

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

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

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

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

HENCE PROVED!!!!!!!