Question

please solve this expansion

(x - 2y – z)²​

Answer 1

$\large\underline{\sf{To\:evaluate - }}$

$\red{\rm :\longmapsto\: {(x - 2y - z)}^{2} }$

$\large\underline{\sf{Solution-}}$

Given expansion is

$\rm :\longmapsto\: {(x - 2y - z)}^{2}$

We know,

$\boxed{ \sf{ \: {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2 bc+ 2ca}}$

So,

Here,

$\rm :\longmapsto\:a = x$

$\rm :\longmapsto\:b = - 2y$

$\rm :\longmapsto\:c = - z$

So, on substituting the values, we get

$\rm :\longmapsto\: {(x - 2y - z)}^{2}$

$\rm \:  =  \: {x}^{2} + {( - 2y)}^{2} + {( - z)}^{2} + 2(x)( - 2y) + 2( - 2y)( - z) + 2( - z)x$

$\rm \:  =  {x}^{2} + {4y}^{2} + {z}^{2} - 4xy + 4yz - 2zx$

Additional Information :-

More Identities to know :-

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

$\boxed{ \bf{ \: {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$

$\boxed{ \bf{ \: {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)}}$

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

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

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

$\boxed{ \bf{ \: {x}^{2} - {y}^{2} = (x + y)(x - y)}}$