Question

Identity :

(x+y)³ =?

Answer 1

$\underline{\underline{\bf SOLUTION :}}$

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

which is also written as ↓

$\bf (x+y)^3=x^{3}+y^{3}+3x^{2}y + 3xy^{2}$

 

Here is the verification :

$\bf(x+y)^3 = (x+y)(x+y)(x+y)\\\\ =[(x+y)(x+y)](x+y)\\\\=[x(x+y) + y(x+y)](x+y)\\\\=[x^{2}+xy + xy+y^{2}](x+y)\\\\=x(x^{2}+xy + xy+y^{2}) + y(x^{2}+xy + xy+y^{2})\\\\=x^3 +x^{2}y+x^{2}y+xy^{2} + x^{2}y + xy^{2}+xy^{2}+y^{3}\\\\=x^{3}+y^{3}+ 3x^{2}y+3xy^{2}$

Hence, proved

$\bf (x+y)^3=x^{3}+y^{3}+3x^{2}y + 3xy^{2}$

Answer 2

Step-by-step explanation:

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

It is an identity

i have mentioned some another identities also