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Question

Factorise 4xyx24y2+z2

A
(zx+2y)(z+x+2y)
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B
(z2x2+2y)(z+x+2y)
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C
=(zx+2y)(z2+x+2y2)
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D
(zx+2y)(z+x22y)
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Solution

The correct option is A (zx+2y)(z+x+2y)
4xyx24y2+z2
=4xyx2(2y)2+z2
=z2[x2+(2y)24xy]
{a22ab+b2=(ab)2}
=z2(x2y)2
{ a22ab+b2=(ab)2}
=z2(x2y)2
{ a2b2=(a+b)(ab)}
=(zx+2y)(z+x2y)

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