Question

Sendo P = m4n2+ 6m8n5 + 3m5n2− m8n6
, Q = 3m4n2
− 6m8
n5 + 5m5n2
+ 4m8
n6
e R = m3
n2
, com m ≠ 0 e n ≠ 0, determine (2P − 3Q) : R.

Answer 1

Resposta:

(2P − 3Q)/R = -14m⁵n⁴+30m⁵n³-9m²-7m

Explicação passo-a-passo:

P=m⁴n²+ 6m⁸n⁵+3m⁵n²−m⁸n⁶

Q = 3m⁴n²− 6m⁸n⁵+ 5m⁵n²+4m⁸n⁶

R=m³n²

(2P − 3Q) : R =?

2P=2(m⁴n²+ 6m⁸n⁵+3m⁵n²−m⁸n⁶)=2m⁴n²+ 12m⁸n⁵+6m⁵n²−2m⁸n⁶

-3Q= -3(3m⁴n²− 6m⁸n⁵+ 5m⁵n²+4m⁸n⁶)= -9m⁴n²+ 18m⁸n⁵- 15m⁵n²-12m⁸n⁶

2P-3Q= (2-9)m⁴n²+(12+18)m⁸n⁵+(6-15)m⁵n²+(-2-12)m⁸n⁶

2P-3Q= -7m⁴n²+30m⁸n⁵-9m⁵n²-14m⁸n⁶

(2P − 3Q)/R =(-7m⁴n²+30m⁸n⁵-9m⁵n²-14m⁸n⁶)/m³n²

(2P − 3Q)/R = -7m⁴⁻³n²⁻²+30m⁸⁻³n⁵⁻²-9m⁵⁻³n²⁻²-14m⁸⁻³n⁶⁻²

(2P − 3Q)/R = -7m¹n⁰+30m⁵n³-9m²n⁰-14m⁵n⁴

(2P − 3Q)/R = -7m+30m⁵n³-9m²-14m⁵n⁴

(2P − 3Q)/R = -14m⁵n⁴+30m⁵n³-9m²-7m