Simplify the following expression:(x+2y)(4x−y)+(2x−y)(y−x)
A
(2x2+10xy−y2)
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B
(x2+5xy−3y2)
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C
(2x2+10xy−3y2)
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D
(x2+6xy−3y2)
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Solution
The correct option is C(2x2+10xy−3y2) (x+2y)(4x−y)+(2x−y)(y−x) =[x(4x−y)+2y(4x−y)]+[2x(y−x)−y(y−x)] =4x2−xy+8xy−2y2+2xy−2x2−y2+xy Grouping all the like terms together and simplifying, =(4x2−2x2)+(−xy+8xy+2xy+xy)+(−2y2−y2) =2x2+10xy−3y2