phân tích thành nhân tử \(\text{x^2 + x + xy - 2}\)
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18 tháng 7 2021
a, \(\dfrac{x^2}{4}-xy+y^2=\left(\dfrac{x}{2}\right)^2-xy+y^2=\left(\dfrac{x}{2}\right)^2-2.\dfrac{x}{2}.y+y^2\)
\(=\left(\dfrac{x^2}{2}-y\right)^2\)
b, \(x^2+x+\dfrac{1}{4}=x^2+\dfrac{1}{2}.2.x+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)
c, \(x^2+2\sqrt{3}x+3=x^2+2\sqrt{3}x+\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)^2\)
d, \(4x^2-1=\left(2x-1\right)\left(2x+1\right)\)
18 tháng 7 2021
`x^2/4-2*x/2*y+y^2`
`=(x/2-y)^2`
`x^2+x+1/4`
`=x^2+2*x*1/2+(1/2)^2`
`=(x+1/2)^2`
`x^2+2sqrt3x+3`
`=x+2xsqrt3+sqrt3^2`
`=(x+sqrt3)^2`
`4x^2-1`
`=(2x)^2-1`
`=(2x-1)(2x+1)`
6 tháng 11 2021
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
12 tháng 10 2021
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
L
4
NV
Nguyễn Việt Lâm
Giáo viên
4 tháng 8 2021
\(=\left(x^2+y^2-x^2y^2-1\right)+\left(xy-x-y+1\right)\)
\(=\left(x^2-1\right)-y^2\left(x^2-1\right)+x\left(y-1\right)-\left(y-1\right)\)
\(=\left(x^2-1\right)\left(1-y^2\right)+\left(x-1\right)\left(y-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(1-y\right)\left(1+y\right)-\left(x-1\right)\left(1-y\right)\)
\(=\left(x-1\right)\left(1-y\right)\left[\left(x+1\right)\left(y+1\right)-1\right]\)
\(=\left(x-1\right)\left(1-y\right)\left(xy+x+y\right)\)
L
4
H
7 tháng 8 2023
`a^3-a^2 x -ay+xy`
`=a^2(a-x)-y(a-x)`
`=(a-x)(x^2-y)`
`x^2-2xy+x-2y`
`= (x^2+x)-(2xy+2y)`
`=x(x+1)-2y(x+1)`
`=(x+1)(x-2y)`
`x^2-2x+2y-xy`
`=x(x-2) + y(2-x)`
`=x(x-2)-y(x-2)`
`=(x-2)(x-y)`
24 tháng 9 2021
\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
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2
7 tháng 8 2023
`@` `\text {Ans}`
`\downarrow`
`x^2 + xy - 2x - 2y`
`= (x^2 - 2x) + (xy - 2y)`
`= x(x - 2) + y(x - 2)`
`= (x + y)(x - 2)`
____
`x^2 - xy - 6x + 6y`
`= (x^2 - 6x) - (xy - 6y)`
`= x(x - 6) - y(x - 6)`
`= (x - y)(x - 6)`
____
`5xy^2 - 5x + y^2 - 1`
`= (5xy^2 + y^2) - (5x + 1)`
`= y^2(5x + 1) - (5x + 1)`
`= (y^2 - 1)(5x + 1)`
`= (y - 1)(y + 1)(5x + 1)`
7 tháng 8 2023
a: =(x^2+xy)-(2x+2y)
=x(x+y)-2(x+y)
=(x+y)(x-2)
b: =(x^2-xy)-(6x-6y)
=x(x-y)-6(x-y)
=(x-y)(x-6)
c: =5xy^2+y^2-5x-1
=y^2(5x+1)-(5x+1)
=(5x+1)(y^2-1)
=(5x+1)(y+1)(y-1)
Đa thức này không phân tích được nhé bạn