Question

Resolve into factor: y2 - 2yz - 4z - 4​

Answer 1

Answer:

$y(y - 2z) - 4(z - 1) \\ (y - 2z)(y - 4)(z - 1)$

Answer 2

SOLUTION

TO DETERMINE

Resolve into factor

$\displaystyle \sf{ {y}^{2} - 2yz - 4z - 4 }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ {y}^{2} - 2yz - 4z - 4 }$

We factorise it as below

$\displaystyle \sf{ {y}^{2} - 2yz - 4z - 4 }$

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

$\displaystyle \sf{ =( {y}^{2} - 2yz + {z}^{2} )- ( {z}^{2} + 4z + 4 )}$

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

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

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

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

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