Selisih 2 Kuadrat
Apabila kita mengalikan a + b dan a — b maka
(a + b)(a — b) = a(a — b) + b(a — b)
= a2 — ab + ba — b2
= a2 — ab + ab — b2
= a2 — b2
Jadi kesimpulannya
a2 — b2 = (a + b)(a — b)
Contoh soal 1:
Faktorkan bentuk berikut
1. x2 — y2
2. 4x2 — y2
3. 9x2 — 16y2
4. 5a2 — 20b2
5. 75a2 — 27b2
Jawab :
1. x2 — y2 = (x + y)(x — y)
2. 4x2 — y2 = (2x)2 — y2
. = (2x + y)(2x — y)
3. 9x2 — 16y2 = (3x)2 — (4y)2
. = (3x + 4y)(3x — 4y)
4. 5a2 — 20b2 = 5(a2 — 4b2)
. = 5(a + 2b)(a — 2b)
5. 75a2 — 27b2 = 3(25a2 — 9b2)
. = 3(5a + 3b)(5a — 3b)
Contoh soal 2:
Faktorkan bentuk berikut
6. x2 — 9
7.y2 — 36
8.4x2 — 81
9.28y2 — 63
10.(x2 + 1)2 — 9x2
Jawab :
6. x2 — 9 = x2 — 32
. = (x + 3)(x — 3)
7. y2 — 36 = y2 — 62
. = (y + 6)(y — 6)
8. 4x2 — 81 = (2x)2 — 92
. = (2x + 9)(2x — 9)
9. 28y2 — 63 = 7(4y2 — 9)
. = 7(2y + 3)(2y — 3)
10. (x2 + 1)2 — 9x2 = (x2 + 1)2 — (3x)2
. =(x2 + 1 + 3x)(x2 + 1 — 3x)
. =(x2 + 3x + 1)(x2 — 3x + 1)