Question

Calculați (fără a efectua înmulțirile)
9×8×7×6-8×7×6×5-7×6×5×4-6×5×4×3-5×4×3×2-4×3×2×1
Dau coroana!​

Answer 1

Răspuns:

0

Explicație pas cu pas:

9×8×7×6 - 8×7×6×5 - 7×6×5×4 - 6×5×4×3 - 5×4×3×2 - 4×3×2×1 =

8×7×6 (9 - 5) - 6×5×4 (7 + 3) - 4×3×2 (5  + 1) =

8×7×6x4 - 6×5×4x10 - 4×3×2x6 =

6x4 (8x7 - 5x10 - 3x2) =

6x4 (56 -50 - 6) =

6x4 x 0 =

0.

Answer 2

Prima diferență este:

$9\cdot8\cdot7\cdot6-8\cdot7\cdot6\cdot5= (4+5)\cdot8\cdot7\cdot6-8\cdot7\cdot6\cdot5= 4\cdot8\cdot7\cdot6+8\cdot7\cdot6\cdot5-8\cdot7\cdot6\cdot5= 8\cdot7\cdot6\cdot4$

A doua diferență este:

$8\cdot7\cdot6\cdot4-7\cdot6\cdot5\cdot4= (3+5)\cdot7\cdot6\cdot4-7\cdot6\cdot5\cdot4= 3\cdot7\cdot6\cdot4+7\cdot6\cdot5\cdot4-7\cdot6\cdot5\cdot4= 7\cdot6\cdot4\cdot3$

A treia diferență este:

$7\cdot6\cdot4\cdot3-6\cdot5\cdot4\cdot3= (2+5)\cdot6\cdot4\cdot3-6\cdot5\cdot4\cdot3= 2\cdot6\cdot4\cdot3+6\cdot5\cdot4\cdot3-6\cdot5\cdot4\cdot3= 6\cdot4\cdot3\cdot2$

A patra diferență este :

$6\cdot4\cdot3\cdot2-5\cdot4\cdot3\cdot2= (1+5)\cdot4\cdot3\cdot2-5\cdot4\cdot3\cdot2= 4\cdot3\cdot2\cdot1+5\cdot4\cdot3\cdot2-5\cdot4\cdot3\cdot2= 4\cdot3\cdot2\cdot1$

Ultima diferență este :

$\it 4\cdot3\cdot2\cdot1-4\cdot3\cdot2\cdot1=0$