\(a,A=x\left(x+5\right)^3:\left(x+5\right)^2+x^2+x\)
\(=x\left(x+5\right)+x^2+x\)
\(=x^2+5x+x^2+x\)
\(=2x^2+6x\)
\(=2x\left(x+3\right)\)
Ta thấy: \(2x\left(x+3\right)⋮x+3\forall x\in Z\)
\(\Rightarrow A⋮x+3\forall x\in Z\)
\(b,B=x^4y^4:y^3x^3+xy+2\)
\(=xy+xy+2\)
\(=2xy+2\)
\(=2\left(xy+1\right)\)
Ta thấy: \(2\left(xy+1\right)⋮xy+1\forall x;y\in Z\)
\(\Rightarrow B⋮xy+1\forall x;y\in Z\)
\(c,C=xy\left(xy+y+1\right)^3:\left(xy+y+1\right)^2+xy\)
\(=xy\left(xy+y+1\right)+xy\)
\(=xy\left(xy+y+1+1\right)\)
\(=xy\left(xy+y+2\right)\)
Ta thấy: \(xy\left(xy+y+2\right)⋮xy+y+2\forall x;y\in Z\)
\(\Rightarrow C⋮xy+y+2\forall x;y\in Z\)
#\(Toru\)
`# \text {DNamNgV}`
`a)`
`A = x(x + 5)^3 \div (x + 5)^2 + x^2 + x`
`= x(x + 5) + x^2 + x`
`= x^2 + 5x + x^2 + x`
`= 2x^2 + 6x`
`= 2x(x + 3)`
Vì `2x(x + 3) \vdots (x + 3)`
`=> A=x(x + 5)^3 \div (x + 5)^2 + x^2 + x \vdots x + 3`
`b)`
`B=x^4y^4 \div y^3x^3 + xy + 2`
`= (x^4 \div x^3)(y^4 \div y^3) + xy + 2`
`= xy + xy + 2`
`= 2xy + 2`
`= 2(xy + 1)`
Vì `2(xy + 1) \vdots xy + 1`
`=> B =x^4y^4 \div y^3x^3 + xy + 2 \vdots xy + 1`
`c)`
`C = xy(xy + y + 1)^3 \div (xy + y + 1)^2 + xy`
`= xy(xy + y + 1) + xy`
`= xy(xy + y + 1 + 1)`
`= xy(xy + y + 2)`
Vì `xy(xy + y + 2) \vdots xy + y + 2`
`=> C = xy(xy + y + 1)^3 \div (xy + y + 1)^2 + xy \vdots xy + y + 2.`
