Help me:
75-(3.\(5^2\)- 4.\(2^3\))
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a: \(=2\sqrt{20\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\cdot\sqrt{20\sqrt{3}}\)
\(=4\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}=-4\sqrt{5\sqrt{3}}\)
b: \(=2\sqrt{5\sqrt{3}}-4\sqrt{2\sqrt{3}}-6\sqrt{5\sqrt{3}}=-4\sqrt{5\sqrt{3}}-4\sqrt{2\sqrt{3}}\)
3.(-4)^3-2.(-5)+(-7)^2.(-6)=3.-64-(-10)+49.(-6)=(-192)-(-10)+(-294)=(-182)+(-294)=(-476)
(5).(-26-25)+(-4).(-51)=5.(-51)+204=(-255)+204=-51
34.(47-75)+47.(75-34)=34.(-28)+47.41=(-952)+1927=975
(-25).(75-45)-75.(45-25)=(-25).30-75.20=(-750)-1500=-2250
a) \(74.42+74.58-400=74.\left(42+58\right)-400\)
\(=74.100-400\)
\(=7400-400\)
\(=7000\)
b) \(75-\left(3.5^2-4.2^3\right)=75-\left(3.25-4.8\right)\)
\(=75-\left(75-32\right)\)
\(=75-75+32\)
\(=32\)
c) \(x-15=-135\)
\(x=-135+15\)
\(x=-120\)
\(\dfrac{1}{5}\left(x+\dfrac{1}{5}\right)+\dfrac{2}{5}\left(x+\dfrac{5}{3}\right)=\dfrac{98}{75}\\ =>\dfrac{1}{5}x+\dfrac{1}{25}+\dfrac{2}{5}x+\dfrac{2}{3}=\dfrac{98}{75}\\ =>\dfrac{3}{5}x=\dfrac{98}{75}-\dfrac{2}{3}-\dfrac{1}{25}=\dfrac{3}{5}\\ =>x=1\)
\(\dfrac{1}{5}\left(x+\dfrac{1}{5}\right)+\dfrac{2}{5}\left(x+\dfrac{5}{3}\right)=\dfrac{98}{75}\\ \Rightarrow\dfrac{1}{5}x+\dfrac{1}{25}+\dfrac{2}{5}x+\dfrac{2}{3}=\dfrac{98}{75}\\ \Rightarrow\left(\dfrac{1}{5}x+\dfrac{2}{5}x\right)+\left(\dfrac{1}{25}+\dfrac{2}{3}\right)=\dfrac{98}{75}\\ \Rightarrow\dfrac{3}{5}x+\dfrac{53}{75}=\dfrac{98}{75}\\ \Rightarrow\dfrac{3}{5}x=\dfrac{98}{75}-\dfrac{53}{75}\\ \Rightarrow\dfrac{3}{5}x=\dfrac{45}{75}=\dfrac{3}{5}\\ \Rightarrow x=\dfrac{3}{5}:\dfrac{3}{5}\\ \Rightarrow x=1\)
\(a,\left|75\right|:\left|-5\right|=75:5=15\)
\(b,\left|2\right|.\left|-3\right|.\left|-4\right|+\left|-11\right|=2.3.4+11=35\)
\(c,\left|-11\right|+\left|-12\right|-\left|-17\right|+\left|9\right|=11+12-17+9=15\)
\(d,\left|35\right|:\left|-7\right|.\left|-2\right|+\left|17\right|=35:7.2+17=27\)
\(e,\left|25-14\right|.\left|-3\right|+\left|-7\right|=11.3+7=40\)
a: \(A=\dfrac{1}{x-1}\cdot5\sqrt{3}\cdot\left|x-1\right|\cdot\sqrt{x-1}\)
\(=\dfrac{5\sqrt{3}}{x-1}\cdot\left(x-1\right)\cdot\sqrt{x-1}=5\sqrt{3}\cdot\sqrt{x-1}\)
b: \(B=10\sqrt{x}-3\cdot\dfrac{10\sqrt{x}}{3}-\dfrac{4}{x}\cdot\dfrac{x\sqrt{x}}{2}\)
\(=10\sqrt{x}-10\sqrt{x}-\dfrac{4\sqrt{x}}{2}=-2\sqrt{x}\)
c: \(C=x-4+\left|x-4\right|\)
=x-4+x-4
=2x-8
\(=\frac{1}{2}\sqrt{16.3}-2\sqrt{25.3}-\frac{\sqrt{3.11}}{\sqrt{11}}+5\sqrt{\frac{1.3+1}{3}}\)
\(=\frac{1}{2}\sqrt{4^2.3}-2\sqrt{5^2.3}-\frac{\sqrt{3}.\sqrt{11}}{\sqrt{11}}+5\sqrt{\frac{4}{3}}\)
\(=\frac{1}{2}.4\sqrt{3}-2.5\sqrt{3}-\sqrt{3}+5\frac{\sqrt{4}}{\sqrt{3}}\)
\(=\frac{4}{2}\sqrt{3}-10\sqrt{3}-\sqrt{3}+5\frac{\sqrt{4}.\sqrt{4}}{\sqrt{3.}\sqrt{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+5\frac{2\sqrt{3}}{3}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+10\frac{\sqrt{3}}{3}\)
\(=\left(2-10-1+\frac{10}{3}\right)\sqrt{3}\)
\(=-\frac{17}{3}\)
\(75-\left(3.5^2-4.2^3\right)=75-\left(3.25-4.8\right)\)
\(=75-\left(75-32\right)=75-75+32=0+32=32\)
75 - ( 3 x 5^2 - 4 x 2^3)
= 75 - ( 3 x 25 - 4 x 8 )
= 75 - (75 - 32 )
= 75 - 43
= 32