Question

factorize y4 + 2y3z -2yz3 - z4​

Answer 1

SOLUTION

TO FACTORISE

$\sf{ {y}^{4} + 2 {y}^{3} z - 2y {z}^{3} - {z}^{4} }$

EVALUATION

Here the given expression is

$\sf{ {y}^{4} + 2 {y}^{3} z - 2y {z}^{3} - {z}^{4} }$

We factorise it as below

$\sf{ {y}^{4} + 2 {y}^{3} z - 2y {z}^{3} - {z}^{4} }$

$\sf{ = {y}^{4} - {z}^{4}+ 2 {y}^{3} z - 2y {z}^{3} }$

$\sf{ = ({y}^{2} + {z}^{2})( {y}^{2} - {z}^{2} )+ 2yz( {y}^{2} - {z}^{2}) }$

$\sf{ = ({y}^{2} - {z}^{2})( {y}^{2} + {z}^{2} + 2yz) }$

$\sf{ = (y + z)(y - z){(y + z)}^{2} }$

$\sf{ = (y + z)(y - z)(y + z)(y + z)}$

$\sf{ = (y - z)(y + z)(y + z)(y + z)}$

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