Question

Escreva os polinômios na forma reduzida.

a) 3 (x5y² - 2xy3) - 2 (x4y - 2xy³) + 4 (x4y - x5y²)

(É "X" na quinta potência,x5y2 --- X na quarta potencia depois o Y,x4y)

b) (a³ + 3a²b + 3ab² + b³) - (a³ - 3a²b + 3ab² - b³)

Answer 1

Oie, Td Bom?!

a)

$= 3 \: . \: (x {}^{5} y {}^{2} - 2xy {}^{3} ) - 2 \: . \: (x {}^{4} y - 2xy {}^{3} ) + 4 \: . \: (x {}^{4} y - x {}^{5} y {}^{2} )$

$= 3x {}^{5} y {}^{2} - 6xy {}^{3} - 2x {}^{4} y + 4xy {}^{3} + 4x {}^{4} y - 4x {}^{5} y {}^{2}$

$= - x {}^{5} y {}^{2} - 2xy {}^{3} + 2x {}^{4} y$

b)

$= (a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} ) - (a {}^{3} - 3a {}^{2} b + 3ab {}^{2} - b {}^{3} )$

$= a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} - a {}^{3} + 3a {}^{2} b - 3ab {}^{2} + b {}^{3}$

$= 6a {}^{2} b + 3ab {}^{2} + 2b {}^{3} - 3ab {}^{3}$

Att. Makaveli1996

Answer 2

a)

3(x⁵y² − 2xy³) − 2(x⁴y − 2xy³) + 4(x⁴y − x⁵y²) =

• Efetue a operação distributiva da multiplicação:

3x⁵y² − 6xy³ − 2x⁴y + 4xy³ + 4x⁴y − 4x⁵y² =

• Reduza os termos semelhantes:
• 3x⁵y² − 4x⁵y² = −x⁵y²
• − 2x⁴y + 4x⁴y = 2x⁴y
• − 6xy³ + 4xy³ = −2xy³

−x⁵y² + 2x⁴y − 2xy³

b)

(a³ + 3a²b + 3ab² + b³) − (a³ − 3a²b + 3ab² − b³) =

a³ + 3a²b + 3ab² + b³ − a³ + 3a²b − 3ab² + b³ =

3a²b + b³ + 3a²b + b³ =

6a²b + 2b³