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Question

# The expression (x2+4y2âˆ’9z2)2âˆ’16x2y2, is equivalent to

A
(x2y+3z)(2x2y3z)(x2y+3z)(x+2y3z)
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B
(x+2y+3z)(x+2y+3z)(x2y+3z)(x+2y3z)
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C
(x2y+3z)(x+2y3z)(x2y+3z)(x2y3z)
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D
(x+2y+3z)(x+2y3z)(x2y+3z)(x2y3z)
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Solution

## The correct option is D (x+2y+3z)(x+2y−3z)(x−2y+3z)(x−2y−3z) (x2+4y2−9z2)2−16x2y2=(x2+4y2−9z2)2−(4xy)2=(x2+4y2−9z2+4xy)(x2+4y2−9z2−4xy)=(x2+4xy+4y2−(3z)2)(x2−4xy+4y2−(3z)2)=(x2+2(x)(2y)+4y2−(3z)2)(x2−2(x)(2y)+4y2−(3z)2)=((x+2y)2−(3z)2)((x−2y)2−(3z)2)=(x+2y+3z)(x+2y−3z)(x−2y+3z)(x−2y−3z)

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