Pada kesempatan kali ini kita akan membicarakan tentang penjabaran bentuk (x + p)(x – p) atau bisa pula ditulis (x + a)(x – a) serta bagaimana penerapannya dlm operasi perkalian aljabar. Untuk lebih jelasnya, perhatikan uraian berikut ini.
Contoh:
□ (x + 5)(x – 5) = x(x – 5) + 5(x – 5)
= x2 – 5x + 5x – 25
= x2 – 25
□ (x + 7)(x – 7) = x(x – 7) + 7(x – 7)
= x2 – 7x + 7x – 49
= x2 – 49
□ (x + 10)(x – 10) = x(x – 10) + 10(x – 10)
= x2 – 10x + 10x – 100
= x2 – 100
Dari beberapa pola di atas, maka mampu kita simpulkan penjabaran bentuk aljabar (x + p)(x – p) yaitu sebagai berikut.
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Penjabaran bentuk (x + p)(x – p):
(x + p)(x – p) = x2 – p2
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Contoh pemakaian penjabaran bentuk (x + p)(x – p) yakni sebagai berikut.
□ (x – 11)(x + 11) = (x)2 – (11)2
= x2 – 121
□ (5 + x)(5 – x) = (5)2 – (x)2
= 25 – x2
□ (xy + 3)(xy – 3) = (xy)2 – (3)2
= x2y2 – 9
□ (7k – 5m)(7k + 5m) = (7k)2 – (5m)2
= 49k2 – 25m2
Contoh Soal & Jawabannya
Jabarkan perkalian berikut dgn memakai pola di atas.
1. (x + 10)(x – 10)
Jawab:
(x + 10)(x – 10) = (x)2 – (10)2
= x2 – 100
2. (x + 8)(x – 8)
Jawab:
(x + 8)(x – 8) = (x)2 – (8)2
= x2 – 64
3. (x + 21)(x – 21)
Jawab:
(x + 21)(x – 21) = (x)2 – (21)2
= x2 – 441
4. (x – 6)(x + 6)
Jawab:
(x – 6)(x + 6) = (x)2 – (6)2
= x2 – 36
5. (x – 15)(x + 15)
Jawab:
(x – 15)(x + 15) = (x)2 – (15)2
= x2 – 225
6. (15 – x)(15 + x)
Jawab:
(15 – x)(15 + x) = (15)2 – (x)2
= 225 – x2
7. (x – 25)(x + 25)
Jawab:
(x – 25)(x + 25) = (x)2 – (25)2
= x2 – 625
8. (13 + x)(13 – x)
Jawab:
(13 + x)(13 – x) = (13)2 – (x)2
= 169 – x2
9. (9 – x)(9 + x)
Jawab:
(9 – x)(9 + x) = (9)2 – (x)2
= 81 – x2
10. (6 – x)(x + 6)
Jawab:
(6 – x)(x + 6) = (6 – x)(6 + x)
= (6)2 – (x)2
= 36 – x2
11. (10 – 7x)(7x + 10)
Jawab:
(10 – 7x)(7x + 10) = (10 – 7x)(10 + 7x)
= (10)2 – (7x)2
= 100 – 49x2
12. (5 + 3x)(5 – 3x)
Jawab:
(5 + 3x)(5 – 3x) = (5)2 – (3x)2
= 25 – 9x2
13. (3x – 2y)(3x + 2y)
Jawab:
(3x – 2y)(3x + 2y) = (3x)2 – (2y)2
= 9x2 – 4y2
14. (5x + 3y)(5x – 3y)
Jawab:
(5x + 3y)(5x – 3y) = (5x)2 – (3y)2
= 25x2 – 9y2
15. (7x + 6y)(-6y + 7x)
Jawab:
(7x + 6y)(-6y + 7x) = (7x + 6y)(7x – 6y)
= (7x)2 – (6y)2
= 49x2 – 36y2
16. (5x + 11y)(11y – 5x)
Jawab:
(5x + 11y)(11y – 5x) = (11y + 5x)(11y – 5x)
= (11y)2 – (5x)2
= 121y2 – 25x2
17. (3xy + 7k)(3xy – 7x)
Jawab:
(3xy + 7k)(3xy – 7x) = (3xy)2 – (7x)2
= 9x2y2 – 49x2
18. (5m + 2xy)(5m – 2xy)
Jawab:
(5m + 2xy)(5m – 2xy) = (5m)2 – (2xy)2
= 25m2 – 4x2y2
19. (5k + 3mn)(5k – 3mn)
Jawab:
(5k + 3mn)(5k – 3mn) = (5k)2 – (3mn)2
= 25k2 – 9m2n2
20. (7p – 2qr)(2qr + 7p)
Jawab:
(7p – 2qr)(2qr + 7p) = (7p – 2qr)(7p + 2qr)
= (7p)2 – (2qr)2
= 49p2 – 4q2r2