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Question

Simplify the following expression:(x+2y)(4xy)+(2xy)(yx)

A
(2x2+10xyy2)
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B
(x2+5xy3y2)
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C
(2x2+10xy3y2)
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D
(x2+6xy3y2)
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Solution

The correct option is C (2x2+10xy3y2)
(x+2y)(4xy)+(2xy)(yx)
=[x(4xy)+2y(4xy)]+[2x(yx)y(yx)]
=4x2xy+8xy2y2+2xy2x2y2+xy
Grouping all the like terms together and simplifying,
=(4x22x2)+(xy+8xy+2xy+xy)+(2y2y2)
=2x2+10xy3y2

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