Hukum Distributif Perkalian terhadap Penjumlahan & Pengurangan (Materi SMP)

Untuk mengetahui bahan hukum distributif perkalian kepada penjumlahan atau pengurangan, coba kalian perhatikan perkalian bentuk aljabar berikut ini.

 4(x + 3) = 4x + 12
 5(x  2) = 5x  10
 -3(2x  8) = -6x + 24
 -7(-3x + 5y) = 21x  35y
 8(2x  3y + 4z) = 16x  24y + 32z
Untuk memahami materi hukum distributif perkalian terhadap penjumlahan atau pengurangan Hukum Distributif Perkalian terhadap Penjumlahan & Pengurangan (Materi SMP)
Sekarang, mari kita kembangkan aturan distributif tersebut untuk memilih hasil perkalian suku dua dgn suku dua berikut ini.
 (x + 3)(x + 5) = x(x + 5)+ 3(x + 5)
= x2 + 5x + 3x + 15
= x2 + 8x + 15

 (x + 3)(x  7) = x(x  7) + 3(x  7)
= x2  7x + 3x  21
= x2  4x  21

 (x  8)(x  5) = x(x  5)  8(x  5)
= x2  5x  8x + 40
= x2  13x + 40

Dari contoh-contoh di atas, maka mampu kita simpulkan ihwal hukum distributif perkalian terhadap penjumlahan, yaitu selaku berikut.
(x + p)(x + q) = x2 + (p + q)x + pq
Untuk setiap p, q  B.

Contoh Soal & Pembahasan
Jabarkan perkalian berikut ini dgn menggunakan pola sifat distributif perkalian terhadap penjumlahan atau pengurangan di atas.
1. (x + 3)(x + 7)
Jawab:
(x + 3)(x + 7) = x2 + (3 + 7)x + (3)(7)
= x2 + 10x + 21

2. (x + 5)(x + 4)
Jawab:
(x + 5)(x + 4) = x2 + (5 + 4)x + (5)(4)
= x2 + 9x + 20

3. (x + 13)(x + 4)
Jawab:
(x + 3)(x + 4) = x2 + (13 + 4)x + (13)(4)
= x2 + 17x + 52

4. (7 + x)(10 + x)
Jawab:
(7 + x)(10 + x) = (x + 7)(x + 10)
= x2 + (7 + 10)x + (7)(10)
= x2 + 17x + 70

5. (x  2)(x + 6)
Jawab:
(x  2)(x + 6) = x2 + (-2 + 6)x + (-2)(6)
= x2 + 4x  12

6. (x  4)(x + 11)
Jawab:
(x  4)(x + 11) = x2 + (-4 + 11)x + (-4)(11)
= x2 + 7x  44

7. (x  8)(x + 13)
Jawab:
(x  8)(x + 13) = x2 + (-8 + 13)x + (-8)(13)
= x2 + 5x  104

8. (x  9)(x  2)
Jawab:
(x  9)(x  2) = x2 + (-9 + (-2))x + (-9)(-2)
= x2  11x + 18

9. (x  11)(x  5)
Jawab:
(x  11)(x  5) = x2 + (-11 + (-5))x + (-11)(-5)
= x2  16x + 55

10. (x  5)(x  2)
Jawab:
(x  5)(x  2) = x2 + (-5 + (-2))x + (-5)(-2)
= x2  7x + 10

11. (12 + x)(8 + x)
Jawab:
(12 + x)(8 + x) = x2 + (12 + 8)x + (12)(8)
= x2 + 20x + 96

12. (8 + x)(9 + x)
Jawab:
(8 + x)(9 + x) = x2 + (8 + 9)x + (8)(9)
= x2 + 17x + 72

13. (14 + x)(3 + x)
Jawab:
(14 + x)(3 + x) = x2 + (14 + 3)x + (14)(3)
= x2 + 17x + 42

14. (x + 8)(-7 + x)
Jawab:
(x + 8)(-7 + x) = x2 + (8 + (-7))x + (8)(-7)
= x2 + x  56
15. (x  16)(x  4)
Jawab:
(x  16)(x  4) = x2 + (-16 + (-4))x + (-16)(-4)
= x2  20x + 64

16. (-2 + x)(x  18)
Jawab:
(-2 + x)(x  18) = x2 + (-2 + (-18))x + (-2)(-18)
= x2  20x + 36

17. (x  12)(x  15)
Jawab:
(x  12)(x  15) = x2 + (-12 + (-15))x + (-12)(-15)
= x2  27x + 180

18. (x  5)(10 + x)
Jawab:
(x  5)(10 + x) = x2 + (-5 + (10))x + (-5)(10)
= x2 + 5x  50

19. (x  17)(x  3)
Jawab:
(x  17)(x  3) = x2 + (-17 + (-3))x + (-17)(-3)
= x2  20x + 51

20. (x  8)(x  14)
Jawab:
(x  8)(x  14) = x2 + (-8 + (-14))x + (-8)(-14)
= x2  22x + 112

21. (x + 18)(x  7)
Jawab:
(x + 18)(x  7) = x2 + (18 + (-7))x + (18)(-7)
= x2 + 11x  126

22. (x + 10)(-5  x)
Jawab:
(x + 10)(-5  x) = x(-5  x) + 10(-5  x)
= -5x  x2  50  10x
= -x2  15x  50

23. (x  5)(x + 8)
Jawab:
(x  5)(x + 8) = x2 + (-5 + 8)x + (-5)(8)
= x2 + 3x  40

24. (-x + 9)(x + 2)
Jawab:
(-x + 9)(x + 2) = -x(x + 2) + 9(x + 2)
= -x2  2x + 9x + 18
= -x2 + 7x + 18

25. (x + 5)(x  13)
Jawab:
(x + 5)(x  13) = x2 + (5 + (-13))x + (5)(-13)
= x2  8x  65

26. (x + 19)(x  3)
Jawab:
(x + 19)(x  3) = x2 + (19 + (-3))x + (19)(-3)
= x2 + 16x  57

27. (x  5)(x + 20)
Jawab:
(x  5)(x + 20) = x2 + (-5 + 20)x + (-5)(20)
= x2 + 15x  100

28. (-2 + x)(x  25)
Jawab:
(-2 + x)(x  25) = x2 + (-2 + (-25))x + (-2)(-25)
= x2  27x + 50

29. (x + 15)(x  3)
Jawab:
(x + 15)(x  3) = x2 + (15 + (-3))x + (15)(-3)
= x2 + 12x  45

30. (x  7)(x  12)
Jawab:
(x  7)(x  12) = x2 + (-7 + (-12))x + (-7)(-12)
= x2  19x + 84