What is the algebraic expression that describes
5x3 + 3y3 + 2z3 subtracted from 6x3 – y3 – z3 and the
result, in turn, subtracted from the sum of the two?
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Answer:First, adding 3x
2
+5xy+7y
2
+3 and 2x
2
−4xy−3y
2
+7, we have
= 3x
2
+5xy+7y
2
+3+2x
2
−4xy−3y
2
+7
= 5x
2
+xy+4y
2
+10
Now,
Subtracting 5x
2
+xy+4y
2
+10 from 9x
2
−8xy+11y
2
= (9x
2
−8xy+11y
2
)−(5x
2
+xy+4y
2
+10)
= 9x
2
−8xy+11y
2
−5x
2
−xy−4y
2
−10
= 4x
2
−9xy+7y
2
−10
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