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Question
Subtract: −2(xy)2 (y3 + 7x2y + 5) from 5y2 (x2y3 – 2x4y + 10x2)
Solution
5y2 (x2y3 − 2x4y + 10x2) − [(−2)(xy)2 (y3 + 7x2y + 5)]
= [5y2(x2y3) − 5y2(2x4y) + 5y2(10x2)] −[(−2)x2y2(y3 + 7x2y + 5)]
= (5y5x2 − 10x4y3 + 50x2y2) − [(−2x2y2)(y3) + (−2x2y2)(7x2y) + (−2x2y2)(5)]
= 5x2y5 − 10x4y3 + 50x2y2 −[−2x2y5 − 14x4y3 −10x2y2]
= 5x2y5 − 10x4y3 + 50x2y2 + 2x2y5 + 14x4y3 + 10x2y2
= (5 + 2)x2y5 + (−10 + 14)x4y3 + (50 + 10)x2y2
= 7x2y5 + 4x4y3 + 60x2y2
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