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\(1.\)
\(4x^2-12x+9\)
\(=\left(2x\right)^2-12x+3^2=\left(2x-3\right)^2\)
\(2.\)
\(7x^2-7xy-5x+5y\)
\(=7x\left(x-y\right)-5\left(x-y\right)\)
\(\left(7x-5\right)\left(x-y\right)\)
\(3.\)
\(x^3-9x\)
\(=x\left(x^2-9\right)\)
\(=x\left(x-3\right)\left(x+3\right)\)
\(4.\)
\(5x\left(x-y\right)-15\left(x-y\right)\)
\(=\left(5x-15\right)\left(x-y\right)\)
\(=5\left(x-3\right)\left(x-y\right)\)
\(5.\)
\(2x^2+x\)
\(=2x\left(x+1\right)\)
\(6.\)
\(x^3+27\)
\(=\left(x+3\right)\left(x^2-3x+9\right)\)
\(7.\)
\(2x^2-4xy+2y^2-32\)
\(=2\left(x^2-2xy+y^2-16\right)\)
\(=2\left[\left(x^2-2xy+y^2\right)-16\right]\)
\(=2\left[\left(x-y\right)^2-4^2\right]\)
\(=2\left(x-y+4\right)\left(x-y-4\right)\)
\(8.\)
\(x^3-4x-3x^2+12\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
\(9.\)
\(2x+2y+x^2-y^2\)
\(=2\left(x+y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+2\right)\)
\(10.\)
\(x^2y-2xy+y\)
\(=y\left(x^2-2x+1\right)\)
\(=y\left(x-1\right)^2\)
\(11.\)
\(y^2+2y\)
\(=y\left(y+2\right)\)
\(12.\)
\(y^2-x^2-6y-6x\)
\(=\left(y-x\right)\left(y+x\right)-6\left(y+x\right)\)
\(=\left(y+x\right)\left(y-x-6\right)\)
\(13.\)
\(x^3-3x\)
\(=x\left(x^2-3\right)\)
\(=x\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)
\(14.\)
\(2x-xy+2z-yz\)
\(=x\left(2-y\right)+z\left(2-y\right)\)
\(=\left(2-y\right)\left(x+z\right)\)
Xong
1)
ĐK: \(x,y\neq 0\); \(x+y\neq 0\)
\(\frac{x^2-y^2}{6x^2y^2}: \frac{x+y}{12xy}\)
\(=\frac{x^2-y^2}{6x^2y^2}. \frac{12xy}{x+y}=\frac{(x-y)(x+y).12xy}{6x^2y^2(x+y)}=\frac{2(x-y)}{xy}\)
2) ĐK: \(x\neq \frac{\pm 1}{2}; 0; 1\)
\(\frac{5x}{2x+1}: \frac{3x(x-1)}{4x^2-1}=\frac{5x}{2x+1}.\frac{4x^2-1}{3x(x-1)}\)
\(=\frac{5x(2x-1)(2x+1)}{(2x+1).3x(x-1)}=\frac{5(2x-1)}{3(x-1)}\)
3) ĐK: \(x\neq \frac{\pm 1}{2}; 0\)
\(\left(\frac{2x-1}{2x+1}-\frac{2x-1}{2x+1}\right): \frac{4x}{10x-5}=0: \frac{4x}{10x-5}=0\)
4) ĐK: \(x\neq \frac{\pm 1}{3}\)
\(\frac{2}{9x^2+6x+1}-\frac{3x}{9x^2-1}=\frac{2}{(3x+1)^2}-\frac{3x}{(3x-1)(3x+1)}\)
\(=\frac{2(3x-1)}{(3x+1)^2(3x-1)}-\frac{3x(3x+1)}{(3x-1)(3x+1)^2}\)
\(=\frac{6x-2-9x^2-3x}{(3x+1)^2(3x-1)}=\frac{-9x^2+3x-2}{(3x-1)(3x+1)^2}\)
5) ĐK: \(x\neq \pm 1; \frac{-7\pm \sqrt{89}}{4}\)
\(\left(\frac{5}{x^2+2x+1}+\frac{2x}{x^2-1}\right): \frac{2x^2+7x-5}{3x-3}\)
\(=\left(\frac{5}{(x+1)^2}+\frac{2x}{(x-1)(x+1)}\right). \frac{3(x-1)}{2x^2+7x-5}\)
\(=\frac{5(x-1)+2x(x+1)}{(x-1)(x+1)^2}. \frac{3(x-1)}{2x^2+7x-5}=\frac{2x^2+7x-5}{(x+1)^2(x-1)}.\frac{3(x-1)}{2x^2+7x-5}\)
\(=\frac{3}{(x+1)^2}\)
1)
a) \(x\left(x-2\right)+x-2=0\)
\(\Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
Vậy x=2 hoặc x=-1
b) \(x\left(x-3\right)+x-3=0\)
\(\Leftrightarrow x\left(x-3\right)+\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
Vậy x=3 hoặc x=-1
1,
a, x(x-2)+x-2=0
<=> (x-2)(x+1)=0
<=> \(\left\{{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\) <=> \(\left\{{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
Vậy S= \(\left\{-1;2\right\}\)
b, x(x-3)+x-3=0
<=> (x-3)(x+1)=0
<=> \(\left\{{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\) <=> \(\left\{{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
Vậy S= \(\left\{-1;3\right\}\)
Bài 2
\(a,x^3+2x^2+x\)
\(=x.\left(x^2+2x+1\right)\)
\(b,xy+y^2-x-y\)
\(=y.\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right).\left(x+y\right)\)
bài 3
\(a,3x.\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x=0\\x^2=4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=2,x=-2\end{cases}}\)
vậy x=0,x=2 hay x=-2
\(b,xy+y^2-x-y=0\)
\(y.\left(x+y\right)-\left(x+y\right)=0\)
\(\left(y-1\right).\left(x+y\right)=0\)
\(\Rightarrow\orbr{\begin{cases}y-1=0\\x+y=0\end{cases}\Rightarrow\orbr{\begin{cases}y=1\\x=-1\end{cases}}}\)
vậy x=-1, y=1