1. Calcula el valor numérico de las siguientes expresiones algebraicas, sabiendo que:
a = 4
b=-7
C=-1
d=6
( todo con procedimiento)
a) 3a²b - 5cd² =
b) 10(d - 5)²a - (c + 3)³ - (b + 6)⁵c²=
c) (-a +b+c-d)(a + c) =
d) 6² – d²
-------------- =
(a + c² – d)
e) a(b-c-3d)
--------------- =
3(4a - 3b)
Respuestas
a) 3a²b - 5cd² =
3(4)²(-7) - 5(-1)(6)² =
-21(16) - (-5)(36) =
-336 - (-180) = -336 + 180 = -156
b) 10(d - 5)²a - (c + 3)³ - (b + 6)⁵c² =
10(6 - 5)²(4) - (-1 + 3)³ - (-7 + 6)⁵(-1)² =
10(1)²(4) - (2)³ - (-1)⁵(-1)² =
40(1) - 8 - (-1)(1) =
40 - 8 - (-1) = 40 - 8 + 1 = 32 + 1 = 33
c) (-a +b+c-d)(a + c) =
(-4 +(-7)+(-1)-6)(4 + -1) =
(-11+(-7))(3) = -18(3) = -54
d) 6² – d² / (a + c² – d) =
6² – (6)² / (4 + (-1)² – 6) =
36 - 36 / (4+1-6) =
0/-1 = 0
e) a(b-c-3d)/3(4a - 3b) =
4(-7-(-1)-3(6)) / 3(4(4) - 3(-7)) =
4(-7+1-18) / 3(16+21) =
4(-24) / 3(37) = -96 / 111 = 0.8648 = 0.865
Respuesta:
3a²b - 5cd² =
3(4)²(-7) - 5(-1)(6)² =
-21(16) - (-5)(36) =
-336 - (-180) = -336 + 180 = -156
b) 10(d - 5)²a - (c + 3)³ - (b + 6)⁵c² =
10(6 - 5)²(4) - (-1 + 3)³ - (-7 + 6)⁵(-1)² =
10(1)²(4) - (2)³ - (-1)⁵(-1)² =
40(1) - 8 - (-1)(1) =
40 - 8 - (-1) = 40 - 8 + 1 = 32 + 1 = 33
c) (-a +b+c-d)(a + c) =
(-4 +(-7)+(-1)-6)(4 + -1) =
(-11+(-7))(3) = -18(3) = -54
d) 6² – d² / (a + c² – d) =
6² – (6)² / (4 + (-1)² – 6) =
36 - 36 / (4+1-6) =
0/-1 = 0
e) a(b-c-3d)/3(4a - 3b) =
4(-7-(-1)-3(6)) / 3(4(4) - 3(-7)) =
4(-7+1-18) / 3(16+21) =
4(-24) / 3(37) = -96 / 111 = 0.8648 = 0.865
Explicación paso a paso: