a) −7x3y2+3x−9x2y+2x3y2−6x+13x2y+x=−7x3y2+2x3y2+3x−6x+x−9x2y+13x2y=−5x3y2−2x+4x2y=−5x3y2+4x2y−2x
b) 12x2y−3xy+6x2y2−12xy2+4xy−8x2y2+6xy2−19x2y+8x2y2=12x2y−19x2y−3xy+4xy+6x2y2−8x2y2+8x2y2−12xy2+6xy2=−7x2y+xy+6x2y2−6xy2
c) −5x5+x+7x4−2−3x+18x5+21x2−3x4+7x=−5x5+18x5+7x4−3x4+21x2+x−3x+7x−2=13x5+4x4+21x2+5x−2
d) (−2x2+y)2−(x+2y2)2−(y−2x2)(x+2y2)+2(y3−x3)−4(x4−y4)=4x4−4x2y+y2−(x2+4xy2+4y4)−(yx+2y3−2x3−4x2y2)+2y3−2x3−4x4+4y4=4x4−4x2y+y2−x2−4xy2−4y4−yx−2y3+2x3+4x2y2+2y3−2x3−4x4+4y4=
Wyrazy podobne:
4x4−4x4=0
−4x2y
y2
−x2
−4xy2
−4y4+4y4=0
−xy
−2y3+2y3=0
2x3−2x3=0
4x2y2
A więc:
−4x2y+y2−x2−4xy2−xy+4x2y2
e) Wykonajmy potęgowanie poszczególnych wyrażeń:
(x2−1)3=x6−3x4+3x2−1
3x2(2x−x2)=6x3−3x4
(2x+1)3=8x3+3⋅4x2+3⋅2x⋅1+1=8x3+12x2+6x+1
Zatem:
x6−3x4+3x2−1−(6x3−3x4)+8x3+12x2+6x+1=x6−3x4+3x2+1−6x3+3x4+8x3+12x2+6x+1
Wyrazy podobne:
x6
−3x4+3x4=0
−6x3+8x3=2x3
3x2+12x2=15x2
6x
−1+1=0
Rozwiązanie to:
x6+2x3+15x2+6x
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