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
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