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Operasi pd aljabar sebenarnya mrpkn materi yg plg banyak keluar pd semua olimpiade mtk sih, jd yg mtk mestinya bab ini bisa :v
A. Penjumlahan:
Ex. (3y+2x)+(5x-3y)
= (3y-3y) + (2x+5x)
= 7x
B. Pengurangan:
WARNING! Kata "oleh" dan "dari" dlm hal ini berbeda, jk "oleh" berarti pengurangan bntk aljabar A dgn bntk B, namun "dari" berarti pengurangan btnk B dgn A, misal:
a) Tentukan hsl pengurangan 5x+y oleh 2x-7y
Mk (5x+y)-(2x-7y)
= (5x-2x) + (y+7y)
= 3x+8y
b) Tentukan hsl pengurangan 5x+y dari 2x-7y
Mk (2x-7y)-(5x+y)
=(2x-5x) + (-7y-y)
= -3x-8y
Tampak dr sini bahwa "oleh" dan "dari" memberikan hasil yg berbeda, shg tdk dpt km samakan
C. Perkalian:
Untuk perkalian bntk aljabar antara suku satu dgn suku dua, dpt menggunakan hukum distributif, yakni:
a) a(b+c) = ab+ac
b) a(b-c) = ab-ac
Sedangkan utk perkalian suku satu dgn suku tiga atau lebih; suku dua atau lebih dgn suku dua atau lebih dpt menggunakan FOIL (First, Outer, Inner, Last) (dlm istilah Indonesia: SCTV)
Ex. (x²-4)(x²-4)
= (x²•x²) + (4•(-x²)) + (4•(-x²)) + (-4•(-4))
= x⁴-4x²-4x²+16
= x⁴-8x²+16
D. Pembagian:
Utk pembagian bntk aljabar, km dpt menggunakan porogapit atau cara Horner. Utk Horner, sy akan membahas itu tersendiri.
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