Question

③ prove that X2-y2=(x-y) (X 2 +X Y+y2)​

Answer 1

Answer:

ok

Step-by-step explanation:

I think your question is to prove

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

so here is the answer -

there is a formula - $(x-y)^{3} = x^{3} - y^{3} - 3xy(x-y)$

from here, we can say that

$x^{3} - y^{3} = (x-y)^{3} + 3xy(x-y)$  [ we transposed  {-3xy(x-y) } ]

Now taking (x-y) common in RHS,

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

now using the identity - $(x-y)^{2} = x^{2} - 2xy + y^{2}$ , we get

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

hence, subtracting 3xy - 2xy we get xy , hence

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

Plz maek me as the brainliest