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1) x²-y² = (x+y)(x-y)
2) (x+y)² = x²+2xy+y²
3) (x-y)² = x²-2xy+y²
4) (a+b)(c+d) = ac+ad+bc+bd
5) a(b+c) = ab+ac
Khusus utk bentuk 2) dan 3) itu bs dicari dgn segitiga Pascal rek :v
Untuk sifat-sifat lainnya merupakan pengembangan dr sifat dasar itu.
Utk pemfaktoran, jenisnya banyak, tp untuk ini hanya akan dibahas sampai pemfaktoran bentuk aljabar dgn pangkat tertingginya 2:
Bentuk (1):
Ex. 3a-9ab = 3a(1)-3a(3b)
= 3a(1-3b)
Bentuk (2):
Ex. 20x⁴+10x³ = 10x³(2x)+10x³(1)
= 10x³(2x+1)
Utk bentuk (3), (4), dan (5) merupakan pemfaktoran kuadrat, little bit tricky :v
Bentuk (3)
Ex. n²-5n+6 = n²-2n-3n+6
= n(n-2)-3(n-2)
= (n-3)(n-2)
Bentuk (4)
Ex. 2x²+7x+5 = 2x²+2x+5x+5
= 2x(x+1)+5(x+1)
= (2x+5)(x+1)
Bentuk (5)
Ex. 12x²+8xy-15y² = 12x²+18xy-10xy-15y²
= 6x(2x+3y)-5y(2x+3y)
= (6x-5y)(2x+3y)
Pada intinya, pemfaktoran bentuk PK(persamaan kuadrat, dmn pangkat tertingginya 2) ada 2 jenis, yaitu:
a) ax²+bx+c, dmn a=1
x²+bx+c = (x+p)(x+q), dmn p+q=b dan pq=c
b) ax²+bx+c, dmn a≠1
ax²+bx+c = ax²+px+qx+c, dmn pq=ac dan p+q=b
Bentuk a) lebih mudah difaktorkan drpd bentuk b) krn km hanya mencari dua bilangan yg jk dikalikan hasilnya adlh konstanta (nilai dr c) dan jk dijumlahkan hasilnya adlh koefisien dr variabel yg pangkatnya satu (nilai dr b)
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