x³ - x - y + y³
K
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12 tháng 10 2021
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
1 tháng 8 2023
\(=\left(x\sqrt{y}-y\sqrt{x}\right)+\left(x-y\right)\)
\(=\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)+\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{xy}+\sqrt{x}+\sqrt{y}\right)\)
10 tháng 8 2021
Ta có: \(2x\left(x-y\right)+y\left(y-x\right)-\left(y-x\right)\)
\(=2x\left(x-y\right)-y\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(2x-y+1\right)\)
24 tháng 9 2021
\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
13 tháng 10 2023
\(=x^2+2xy+y^2-y\left(x^2-2xy+y^2\right)=x^2+2yx+y^2-yx^2-2xy^2-y^3\)
\(=y^2\left(1-y\right)+x^2\left(1-y\right)+2xy\left(1-y\right)\)\(=\left(1-y\right)\left(x^2+y^2+2xy\right)=\left(1-y\right)\left(x+y\right)^2\)
K
5 tháng 1 2022
\(x\left(x-y\right)+7\left(y-x\right)\)
\(=x^2-xy+7y-7x\)
\(=x^2-7x-xy+7y
\)
\(=\left(x^2-7x\right)-\left(xy-7y\right)\)
\(=x\left(x-7\right)-y\left(x-7\right)\)
\(=\left(x-7\right)\left(x-y\right)\)
KK
14 tháng 9 2021
x2(x - y) + 49(y - x)
= x2(x - y) - 49(x - y)
= (x2 - 49)(x - y)
= (x - 7)(x + 7)(x - y)
\(x^3\) - \(x-y\) + y3
= (\(x^3\) + y3) - (\(x+y\))
= (\(x+y\)).(\(x^2\) - \(xy\) + y2) - (\(x+y\))
= (\(x+y\)).(\(x^2\) - \(xy+y^2\) - 1)
\(x^3-x-y+y^3\)
\(=\left(x^3+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)