Question

identities of polynomial ​

Answer 1

$Identity\:I$

$({x + y})^{2} = {x}^{2} + 2xy2 {y}^{2}$

$Identity \:II$

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

$Identity \:III$

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

$Identity \:IV$

$(x + a)(x + b) = {x}^{2} + (a + b)x + ab$

$Identity \:V$

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

$Identity \:VI$

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

$Identity\: VII$

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

$Identity\: VIII$

${x}^{3} + {y}^{3} + {z}^{3} - 3xyz = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

hope it helps u...!!

Answer 2

$Identity I$

$({x + y})^{2} = {x}^{2} + 2xy2 {y}^{2}$

$Identity II$

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

$Identity III$

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

$Identity IV$

$(x + a)(x + b) = {x}^{2} + (a + b)x + ab$

$Identity V$

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

$Identity VI$

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

$Identity VII$

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

$Identity VIII$

${x}^{3} + {y}^{3} + {z}^{3} - 3xyz = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

hope it helps u...!!