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Bài 5:
Ta có: \(\dfrac{158-x}{31}+\dfrac{185-x}{29}+\dfrac{208-x}{27}+\dfrac{227-x}{25}=10\)
\(\Leftrightarrow\dfrac{158-x}{31}+\dfrac{185-x}{29}+\dfrac{208-x}{27}+\dfrac{227-x}{25}-10=0\)
\(\Leftrightarrow\dfrac{158-x}{31}-1+\dfrac{185-x}{29}-2+\dfrac{208-x}{27}-3+\dfrac{227-x}{25}-4=0\)
\(\Leftrightarrow\dfrac{127-x}{31}+\dfrac{127-x}{29}+\dfrac{127-x}{27}+\dfrac{127-x}{25}=0\)
\(\Leftrightarrow\left(127-x\right)\left(\dfrac{1}{31}+\dfrac{1}{29}+\dfrac{1}{27}+\dfrac{1}{25}\right)=0\)
mà \(\dfrac{1}{31}+\dfrac{1}{29}+\dfrac{1}{27}+\dfrac{1}{25}>0\)
nên 127-x=0
hay x=127
Vậy: S={127}
Bài 2:
Ta có: \(2\left(5m+2\right)^2-8\)
\(=2\cdot\left(25m^2+20m+4\right)-8\)
\(=50m^2+40m\)
\(=10m\left(5m+4\right)⋮10\)
Bài 4:
b: \(B=\left(x-y\right)\left(x^2+xy+y^2\right)+2y^3-5-\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=x^3-y^3+2y^3-5-x^3-y^3\)
=-5
c: \(C=\left(x-1\right)^3-\left(x+1\right)^3-6\left(x+1\right)\left(x-1\right)\)
\(=x^3-3x^2+3x-1-x^3-3x^2-3x-1-6\left(x^2-1\right)\)
\(=-6x^2-2-6x^2+6\)
\(=-12x^2+4\)
\(4,\\ a,=\left(x-3\right)^2\\ b,=\left(3x+1\right)^2\\ c,=\left(5x-3y\right)\left(5x+3y\right)\\ d,=\left(x-2\right)\left(x^2+2x+4\right)\\ e,=\left(2x+1\right)\left(4x^2-2x+1\right)\\ f,=\left(x-3\right)^3\\ g,=\left(a+b-1\right)^2\\ h,=\left(a+2\right)^3\\ i,=\left(x^2+4-4x\right)\left(x^2+4+4x\right)=\left(x-2\right)^2\left(x+2\right)^2\\ u,=\left(x+y+z-2z\right)\left(x+y+z+2z\right)\\ =\left(x+y-z\right)\left(x+y+3z\right)\)
\(5,\\ a,=\left(x+y\right)^2=\left(2004-2003\right)^2=1^2=1\\ b,=\left(x+4\right)^3=\left(-4+4\right)^3=0^3=0\)