Đáp án:
$1)
a)
A=\dfrac{-1}{72}\\
b)
B=32\\
2)
P(-1)=4\\
P\left ( \dfrac{1}{2} \right )=\dfrac{25}{16}\\
Q(-2)=1\\
Q(1)=2\\
3)
a)
A=5\\
c)
P=\dfrac{-1}{18}\\
b)
B=\dfrac{5}{3}\\
d)
D=\dfrac{-1}{9}\\$
Giải thích các bước giải:
$1)
a)
A=3.\dfrac{1}{2}^3.\dfrac{-1}{3}+6.\dfrac{1}{2}^2.\left ( -\dfrac{1}{3} \right )^2+3.\dfrac{1}{2}.\left ( -\dfrac{1}{3} \right )^3\\
=\dfrac{-1}{8}+6.\dfrac{1}{4}.\dfrac{1}{9}+\dfrac{3}{2}.\dfrac{-1}{27}\\
=\dfrac{-1}{8}+\dfrac{1}{6}+\dfrac{-1}{18}\\
=\dfrac{-9}{72}+\dfrac{12}{72}+\dfrac{-4}{72}\\
=\dfrac{-1}{72}\\
b)
B=(-1)^2.3^2+(-1).3+(-1)^3+3^3\\
=1.9-3-1+27\\
=32\\
2)
P(-1)=(-1)^4+2.(-1)^2+1=1+2+1=4\\
P\left ( \dfrac{1}{2} \right )=\dfrac{1}{2}^4+2.\dfrac{1}{2}^2+1\\
=\dfrac{1}{16}+\dfrac{1}{2}+1\\
=\dfrac{1}{16}+\dfrac{8}{16}+\dfrac{16}{16}\\
=\dfrac{25}{16}\\
Q(-2)=(-2)^4+4.(-2)^3+2.(-2)^2-4.(-2)+1\\
=16-4.8+2.4+8+1\\
=1\\
Q(1)=1^4+4.1^3+2.1^2-4.1+1\\
=1+4+2-4+1\\
=2\\
3)
a)
A=2.2^2-\dfrac{1}{3}.9\\
=2.4-3=5\\
c)
P=2.\left (\dfrac{-1}{2} \right )^2+3.\dfrac{-1}{2}.\dfrac{2}{3}+\dfrac{2}{3}^2\\
=2.\dfrac{1}{4}-1+\dfrac{4}{9}\\
=\dfrac{1}{2}-1+\dfrac{4}{9}\\
=\dfrac{9}{18}-\dfrac{18}{18}+\dfrac{8}{18}\\
=\dfrac{-1}{18}\\
b)
B=\dfrac{1}{2}.(-2)^2-3.\left ( -\dfrac{1}{3} \right )^2\\
=\dfrac{1}{2}.4-3.\dfrac{1}{9}\\
=2-\dfrac{1}{3}\\
=\dfrac{6}{3}-\dfrac{1}{3}\\
=\dfrac{5}{3}\\
d)
D=12.\dfrac{-1}{3}.\left (\dfrac{-1}{6} \right )^2\\
=-4.\dfrac{1}{36}\\
=\dfrac{-1}{9}\\$
