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Question

Factorise: x2+9y2−25m2−16n2+6xy+40mn.

A
(2x+3y+5m+4m)(x3y2m+4n)
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B
(2x+3y+4m4m)(x+3y5m4n)
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C
(x+3y+5m4n)(x+3y5m+4n)
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D
(x+y+3m4m)(x+3y+5m+4n)
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Solution

The correct option is C (x+3y+5m4n)(x+3y5m+4n)
x2+9y225m216n2+6xy+40mn
=x2+6xy+9y225m2+40mn16n2
=(x2+6xy+9y2)(25m240mn+16n2)
=(x+3y)2(5m4n)2
=[(x+3y)+(5m4n)][(x+3y)(5m4n)]
=(x+3y+5m4n)(x+3y5m+4n)

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