Question

can you please tell me the the answer
please write the steps also

Answer 1

HEY MATE HERE IS UR ANSWER

WE NEED TO FACTORIZE

$xy( {z}^{2} + 1) \: + z( {x}^{2} + {y}^{2} )$

NOW FOR FACTORISING IT FURTHER WE NEED TO OPEN THE BRACKET AND FIND THE PRODUCTS

THAT IS EQUAL TO

$xy {z}^{2} + xy + {z}{ {x}^{2} } + z{y}^{2}$

NOW WE NEED TO RE ARRANGE THIS TERMS

SO WE HAVE

$xy {z}^{2} + z {x}^{2} + z {y}^{2} + xy \: \: \: ( \: re \: arranged \: terms \: )$

NOW WE NEED TO REGROUP THE TERMS THEREFORE WE HAVE

$(xy {z}^{2} + z {x}^{2} ) \: + \: (z {y}^{2} + xy)$


NOW TAKING COMMON

$zx \: from \: first \: group$
$and \: y \: from \: second \: group$

THERE FOR WE HAVE

$zx(yz + x) + y(yz + x)$

WHICH IS EQUAL TO


$(yz + x) \: (zx + y)$
THERE FOR

OPTION C IS CORRECT

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