Úpravy výrazů Zadání
Upravte na součin
1. x6y3 — z9
2. x12 + yez9
3. 64- 27x3
4. 125y3 + 8
5. 64y3 - 144y2 + 10% - 27
6. 8í3 + 60t2 + 150* + 125
7. 8x3 - 36x2y + 5Axy2 - 27y3
8. x2 + 3x + 2xy + 6y
9. 3xy2 + 6x - y2 - 2
10. 9x2y + 18x2 - 4y - 8
11. -8x3y + 32x3 -y + 4
12. 8x3 + 12x2y - 18xy2 - 27y3
13. 2í3 - 3í2 + 8í - 12 *14. í4 + 4
*15. 81x4 + 64
Výsledky
1. x6y3 — z9 = {x2yý — (z3)3 = (x2y — z3)   (x2y)2 + x2yz3 + (z3)2 = (x2y — z3) (x4y2 + x2yz3 + z6)
2. x12 + y6z9
(x4)3 + (y2z3)3
(x4 + y2z3)
(x4Ý — x4y2z3 + (y22;3)2
+ y2z3) (x8 — x4y2z3 + y4z6)
3. 64 - 27x3 = 43 - (3x)3 = (4 - 3x) 42 + 4 • (3x) + (3x)2  = (4 - 3x) (16 + 12x + 9x2)
4. 125y3 + 8 = (5y)3 + 23 = (5y + 2) [(5y)2 - (5y) • 2 + 22] = (5y + 2) (25y2 - 10y + 4)
5. 64y3 - 144y2 + 108y - 27 = (4y)3 - 3 • (4y)2 • 3 + 3 • 4y • 32 - 33 = (4y - 3)3
6. 8í3 + 60í2 + 150* + 125 = (2í)3 + 3 • (2í)3 • 5 + 3 • 2t ■ 52 + 53 = (2* + 5)3
7. 8x3 - 36x2y + 54xy2 - 27y3 = (2x)3 - 3 • (2x)2 • 3y + 3 • 2y ■ (3y)2 - (3y)3 = (2x - Syf
8. x2 + 3x + 2xy + 6y = x (x + 3) + 2y (x + 3) = (x + 2y) (x + 3)
9. 3xy2 + 6x - y2 - 2 = 3x (y2 + 2) - {y2 + 2) = (3x - 1) {y2 + 2) 10. 9x2y + 18x2 - 4y - 8 = 9x2 (y + 2) - 4 (y + 2) = (y + 2) (9x2 - 4)
(y+ 2) (3x)
(y + 2) (3x - 2) (3x + 2)
11. -8x3y+32x3-y+4 = 8x3 (4 - y) + (4 - y) = (8x3 + l) (4 - y) =  (2x)3 + l3 (4-y)
(4 - y) = (2x + 1) (4x2 - 2x + 1) (4 - y)
(2x + 1) {2xf -2X-1 + 12
12. 8x3 + 12x2y - 18xy2 - 27y3 = 4x2 {Ax + 3y) - 9y2 {2x + 3y) = (4x2 - 9y2) {2x + 3y) :
=  {2xf - (3y)2 {2x + 3y) = {2x - 3y) {2x + 3y) {2x + 3y) = {2x - 3y) {2x + 3y)2
13. 2í3 - 3í2 + 8í - 12 = t2 (2í - 3) + 4 (2í - 3) = (í2 + 4) (2í - 3)
<14. í4 + 4 = (í2)2 + 2 • (í2) • 2 + 22 - 4í2 = (í2 + 2)2 - (2í)2 = (í2 - 2í + 2) (í2 + 2í + 2)
'15. 81x4 + 64
Í9x2)2 + 2- (9x2) -8 + 82
144x"
(9x2 - 12x + 8) (9x2 + 12x + 8)
(9x2 + 8) - (12xý
2