What should be subtracted from 2x3-3x2y+2xyz +3y3to get x3-2x2y+3xy2+4y3?
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Answer:
Let the polynomial to be subtracted be M
According to question,
2x
3
−3x
2
y+2xy
2
+3y
3
−M=x
3
−2x
2
y+3xy
2
+4y
3
⇒M=(2x
3
−3x
2
y+2xy
2
+3y
3
)−(x
3
−2x
2
y+3xy
2
+4y
3
)
⇒M=2x
3
−3x
2
y+2xy
2
+3y
3
−x
3
+2x
2
y−3xy
2
−4y
3
Collecting like terms,
⇒M=2x
3
−x
3
−3x
2
y+2x
2
y+2xy
2
−3xy
2
+3y
3
−4y
3
⇒M=x
3
−x
2
y−xy
2
−y
3
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