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Question

Factorise:

(x2+4y29z2)216x2y2

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Solution

(x2+4y29z2)216x2y2=(x2+(2y)2(3z)2)2(4xy)2 , using identity (a2b2)=(a+b)(ab)=(x2+(2y)2(3z)24xy)(x2+(2y)2(3z)2+4xy)=(x2+(2y)24xy(3z)2)(x2+(2y)2+4xy(3z)2)=((x2y)2(3z)2)((x+2y)2(3z)2)=[(x2y3z)(x2y+3z)][(x+2y3z)(x+2y+3z)]=(x2y3z)(x2y+3z)(x+2y3z)(x+2y+3z)


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