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Question

Factorize: x2+4y2−9z2−4xy

A
[(x4y3z)(x4y+3z)]
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B
[(x2y3z)(x2y+3z)]
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C
[(x+2y3z)(x+2y+3z)]
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D
none
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Solution

The correct option is A [(x2y3z)(x2y+3z)]
The given expression x2+4y29z24xy can be factorized as shown below:

x2+4y29z24xy=(x2+4y24xy)9z2=[x2+(2y)2(2×x×2y)]9z2=(x2y)29z2((ab)2=a2+b22ab)=(x2y)2(3z)2=(x2y3z)(x2y+3z)(a2b2=(ab)(a+b))

Hence, x2+4y29z24xy=(x2y3z)(x2y+3z).

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