Question

Wykonaj redukcję wyrazów podobnych i oblicz wartość liczbową wyrażenia dla a= -3, b= -⅙, c= 2:
a) 2a-3b+4c²-7a+12b-3½c²
b) -3abc + 2a²b²-3ab-a²b²+4abc
c) 7ac - 4ab + 8bc-6ac+ 12ab - 10bc
d) -2a³b²c+2ab²c³-3a²b²c²+ 4a³b²c
e) 0,6b²c-0,2a²b+1,4cb²-0,8ba²-jedna dziewiąta
f) -3abc³+2ba²c-6c³ab-4a²bc-bac²

Answer 1

A= -3, b= -⅙, c= 2:
a) 2a-3b+4c²-7a+12b-3½c²
-5a+9b + ½c²
-5 * (-3) + 9 * (-⅙) + ½ * 2² =
= 15 + ³/₂ + ½*4 = 15 + 1½ + 2 = 18½

b) -3abc + 2a²b²-3ab-a²b²+4abc =
= abc + a²b² -3ab
-3 * (-⅙) * 2 + (-3)² * (-⅙)² - 3 *(-3) * (-⅙) =
= -6 * (-⅙) + 9* ¹/₃₆ + 9* (-⅙) =
= 1+ ¼ - ³/₂ = 1 + ¼ - ⁶/₄ = 1 - ⁵/₄ = -¼

c) 7ac - 4ab + 8bc-6ac+ 12ab - 10bc
= ac+ 8ab-2bc
(-3) * 2 + 8 * (-3) * (-⅙) - 2 * (-⅙) * 2=
= -6 +6 * (-⅙) - 4 * (-⅙)=
=-6-1 + ⅔ = -7 +⅔ = -6⅓

d) -2a³b²c+2ab²c³-3a²b²c²+ 4a³b²c
= 2 a³b²c + 2ab²c³-3a²b²c²
2 * (-3)³ * (-⅙)² * 2 + 2 * (-3) * (-⅙)² * 2³ - 3 * (-3)² *(-⅙)² * 2² =
=4*(-27)* ¹/₃₆ -6 * ¹/₃₆ * 27 -3 * 9 * ¹/₃₆ * 4 =
= 4 * ¾ - 6 * ¾ - ¾ *4 =
= 3 -⁹/₂ -3 = - 4½

e) 0,6b²c-0,2a²b+1,4cb²-0,8ba²-jedna dziewiąta
= 2 b²c - a²b + ⁸/₉
2 * (-⅙)² * 2 - (-3)²* (-⅙) + ⁸/₉ =
= 4*¹/₃₆ -9 * (-⅙) + ⁸/₉ =
=¹/₉ + ³/₂ + ⁸/₉ = ²/₁₈ + ²⁷/₁₈ + ¹⁶/₁₈ = ⁴⁵/₁₈ = 3

f) -3abc³+2ba²c-6c³ab-4a²bc-bac²
= -9abc-2a²bc-bac²
-9 * (-3) * (-⅙) *2 - 2 * (-3)² * (-⅙) * 2 - (-⅙) * (-3) * 2² =
= -9 * -6 * (-⅙) - 4 * 9 * (-⅙) - ½ * 4 =
= -9 * 1 - 4 * (-³/₂) - 2 = -9 +6 - 2 = -5

Answer 2

A) 2a-3b+4c²-7a+12b-3½c²=-5a+9b+½c²=(-5)*(-3)+9*(-⅙)+½*2²=
=15-3/2+½*4=15-3/2+2=15-1½+2=17-1½=15½

b) -3abc + 2a²b²-3ab-a²b²+4abc=abc-3ab+a²b²=[(-3)*(-⅙)*2]-[3*(-3)*(-⅙)]+[(-3)²*(-⅙)²]=1-1½+¼=1-6/4+¼=5/4-6/4=-¼

c) 7ac - 4ab + 8bc-6ac+ 12ab - 10bc=ac+8ab-2bc=[(-3)*2]+[8*(-3)*(-⅙)]-[2*(-⅙)*2]=(-6)+[(-24)*(-⅙)]-(⅓*2)=(-6)+(-4)-⅔=-6-4-⅔=-10⅔

d) -2a³b²c+2ab²c³-3a²b²c²+ 4a³b²c=2ab²c-3a²b²c²+2ab²c³=[2*(-3)*(-⅙)²*2]-[3*(-3)²*(-⅙)²*2²]+[2*(-3)*(-⅙)²*2³=[(-6)*(-⅙)*2]-[3*9*(-⅙)*4]+[(-6)*(-1/36)*8]=2/6-3+1½=2/6-3+1 3/6=1 5/6-3=-1⅙