Tabel 3.6 Model Perkalian Bentuk Aljabar
AXB
B
B (Dengan Rumus yang (Dengan Cara
Ditemukan)
Singkat)
x + 1 x? + (-1 + 1)x + (-1)
x?_1
1.
x-1
2.
x-3
x + 3
x2 + (-3+3)x + (-3)(3)
x²9
3.
2x – 1
2x + 1
4×2 + (2-2)x + (-1)(1)
4.
3x-2 3x + 2
5.
4X-3 4x + 3
6.
5x – 4 5x + 4
7.
3x – 4y|3x + 4y
8.
3x – 5y3x + 5y
.
9.
6x – 2y|6x + 2y
10.
ax-b
ax + b
* Lihat di gambar saja agar jelas, tolong bantu. jawab satu saja juga gak papa. Atau tolong berikan caranya / prinsip cara kerjanya
No.
Jawaban:
4. 9x² + (6 – 6)x + (-1) (1) dan 9x² – 1
5. 16x² + (12 – 12)x + (-3) (3) dan 16x² – 9
6. 25x² + (20 – 20)x + (-4) (4) dan 9x² – 16
7. 9x² + (12 – 12)xy + (-4y) (4y) dan 9x² – 16y²
8. 9x² + (15 – 15)xy + (-5y) (5y) dan 9x² – 25y²
9. 36x² + (12 – 12)xy + (-2y) (2y) dan 9x² – 4y²
10. ax² + (ab – ab)x + (-b) (b) dan ax² – b²
Penjelasan dengan langkah-langkah:
4. (3x – 2) (3x + 2)
(3x – 2) * (3x + 2)
= (3x * 3x) + (3x * 2) + (-2 * 3x) + (-2 * 2)
= 9x² + 6x – 6x + (-2 * 2)
= 9x² + (6 – 6)x + (-1) (1)
9x² + (6 – 6)x + (-1) * (1)
= 9x² + 0x + (-1)
= 9x² – 1
5. (4x – 3) (4x + 3)
(4x – 3) * (4x + 3)
= (4x * 4x) + (4x * 3) + (-3 * 4x) + (-3 * 3)
= 16x² + 12x – 12x + (-3 * 3)
= 16x² + (12 – 12)x + (-3) (3)
16x² + (12 – 12)x + (-3) * (3)
= 16x² + 0x + (-9)
= 16x² – 9
6. (5x – 4) (5x + 4)
(5x – 4) * (5x + 4)
= (5x * 5x) + (5x * 4) + (-4 * 5x) + (-4 * 4)
= 25x² + 20x – 20x + (-4 * 4)
= 25x² + (20 – 20)x + (-4) (4)
25x² + (20 – 20)x + (-4) * (4)
= 25x² + 0x + (-16)
= 9x² – 16
7. (3x – 4y) (3x + 4y)
(3x – 4y) * (3x + 4y)
= (3x * 3x) + (3x * 4y) + (-4y * 3x) + (-4y * 4y)
= 9x² + 12xy – 12xy + (-4y * 4y)
= 9x² + (12 – 12)xy + (-4y) (4y)
9x² + (12 – 12)xy + (-4y) * (4y)
= 9x² + 0x + (-16y²)
= 9x² – 16y²
8. (3x – 5y) (3x + 5y)
(3x – 5y) * (3x + 5y)
= (3x * 3x) + (3x * 5y) + (-5y * 3x) + (-5y * 5y)
= 9x² + 15xy – 15xy + (-5y * 5y)
= 9x² + (15 – 15)xy + (-5y) (5y)
9x² + (15 – 15)xy + (-5y) * (5y)
= 9x² + 0x + (-25y²)
= 9x² – 25y²
9. (6x – 2y) (6x + 2y)
(6x – 2y) * (6x + 2y)
= (6x * 6x) + (6x * 2y) + (-2y * 6x) + (-2y * 2y)
= 36x² + 12xy – 12xy + (-2y * 2y)
= 36x² + (12 – 12)xy + (-2y) (2y)
36x² + (12 – 12)xy + (-2y) * (2y)
= 36x² + 0x + (-4y²)
= 9x² – 4y²
10. (ax – b) (ax + b)
(ax – b) * (ax + b)
= (ax * ax) + (ax * b) + (-b * ax) + (-b * b)
= ax² + abx – abx + (-b * b)
= ax² + (ab – ab)x + (-b) (b)
ax² + (ab – ab)x + (-b) * (b)
= ax² + 0x + (-b²)
= ax² – b²