4-1
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1. Korruta.
a) (m + n)(a + b)
Lahendus: (m + n)(a + b) = am + bm + an + bn
b) (– d + 2)(a + b)
Lahendus: (– d + 2)(a + b) = –ad – bd + 2a + 2b
c) (a + c)(s – t)
Lahendus: (a + c)(s – t) = as – at + cs – ct
d) (p + 6)(1 – m)
Lahendus: (p + 6)(1 – m) = p – mp + 6 – 6m
2. Korruta.
a) (x – 2)(x + 1)
Lahendus: (x – 2)(x + 1) = x2 + x – 2x – 2 = x2 – x – 2
b) (x + 3)(x + 2)
Lahendus: (x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6
c) (–3x – 2)(x – 2)
Lahendus: (–3x – 2)(x – 2) = –3x2 + 6x – 2x + 4 = –3x2 + 4x + 4
d) (a + 5)(2a – 4)
Lahendus: (a + 5)(2a – 4) = 2a2 – 4a + 10a – 20 = 2a2 + 6a – 20
e) (2u – 1)(3x – 1)
Lahendus: (2u – 1)(3x – 1) = 6ux – 2u – 3x + 1
f) (4y + 3)(a + 1)
Lahendus: (4y + 3)(a + 1) = 4ay + 4y + 3a + 3
3. Lihtsusta avaldis.
a) (a – b)(b – ab) + ab(a – b)
Lahendus: (a – b)(b – ab) + ab(a – b) =
= ab – a2b – b2 + ab2 + a2b – ab2 =
= – b2 + ab
b) 2a + 9 – (a + 1)(– a + 1)
Lahendus: 2a + 9 – (a + 1)(– a + 1) =
= 2a + 9 – (–a2 + a – a + 1) =
= 2a + 9 + a2 – 1 = a2 + 2a + 8
c) (x – 2)(x + 2) – (2x + 4)(x – 1)
Lahendus: (x – 2)(x + 1) – (2x + 4)(x – 1) =
= x2 + x – 2x – 2 – (2x2 – 2x + 4x – 4) =
= x2 – x – 2 – 2x2 + 2x – 4x + 4 = –x2 – 3x + 2
d) (n + 2)(m – 2) + 2(2 – n)
Lahendus: (n + 2)(m – 2) + 2(2 + n) =
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