Question

xy(x+4y+z)^2-4xy(x+4y+z)​

Answer 1

Factorise -

$\sf{xy {(x + y + z)}^{2} - 4xy(x + y + 4z)}$

Solution -

$\sf{xy {(x + y + z)}^{2} - 4xy(x + y + 4z)} \\ \\ \sf{(x + y + 4z)(xy(x + y + 4z) - 4)} \\ \\ \sf{(x + y + 4z)( {x}^{2}y - x {y}^{2} + 4xyz - 4) } \:....(a)$

Additional information -

$\sf{ { (a+b)} ^ 2 = a^2 + 2ab + b^2 } \\ \\ \sf{ { (a-b)}^2 = a^2 - 2ab + b^2 }$

$\sf{ a^2 - b^2 = (a-b)(a+b) } \\ \\ \sf{ {( a+b+c)}^2 = a^2 + b^2 + c^2 + 2ab + 2bc +2ac }$

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