Escreva os polinômios de forma reduzida a) n) c)
Soluções para a tarefa
Explicação passo-a-passo:
a)
= 3 \: . \: (x {}^{5} y {}^{2} - 2xy {}^{3} ) - 2 \: . \: (x {}^{4} y - 2xy {}^{3} ) + 4 \: . \: (x {}^{4} y - x {}^{5} y {}^{2} )=3.(x
5
y
2
−2xy
3
)−2.(x
4
y−2xy
3
)+4.(x
4
y−x
5
y
2
)
= 3x {}^{5} y {}^{2} - 6xy {}^{3} - 2x {}^{4} y + 4xy {}^{3} + 4x {}^{4} y - 4x {}^{5} y {}^{2}=3x
5
y
2
−6xy
3
−2x
4
y+4xy
3
+4x
4
y−4x
5
y
2
= - x {}^{5} y {}^{2} - 2xy {}^{3} + 2x {}^{4} y=−x
5
y
2
−2xy
3
+2x
4
y
b)
= (a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} ) - (a {}^{3} - 3a {}^{2} b + 3ab {}^{2} - b {}^{3} )=(a
3
+3a
2
b+3ab
2
+b
3
)−(a
3
−3a
2
b+3ab
2
−b
3
)
= a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} - a {}^{3} + 3a {}^{2} b - 3ab {}^{2} + b {}^{3}=a
3
+3a
2
b+3ab
2
+b
3
−a
3
+3a
2
b−3ab
2
+b
3
= 6a {}^{2} b + 3ab {}^{2} + 2b {}^{3} - 3ab {}^{3}=6a
2
b+3ab
2
+2b
3
−3ab
3