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bài 11
a) \(x^2-xy+x\\ =x\left(x-y+1\right)\)
b)
\(x^2-2xy-4+y^2\\ =\left(x^2-2xy+y^2\right)-4\\ =\left(x-y\right)^2-4\\ =\left(x-y-2\right)\left(x-y+2\right)\)
c)
\(x^3-x^2-16x+16\\ =x^2\left(x-1\right)-16\left(x-1\right)\\ =\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
bài 12
\(2x\left(x-5\right)-x\left(3+2x\right)=26\)
\(2x^2-10x-3x-2x^2=26\)
\(-13x=26\\ x=-2\)
b)
\(2\left(x+5\right)-x^2-5x=0\\ 2\left(x+5\right)-x\left(x+5\right)=0\\ \left(x+5\right)\left(2-x\right)=0\\ \left[{}\begin{matrix}x+5=0\\2-x=0\end{matrix}\right.\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
d: Ta có: \(4x\left(2x+3\right)-8x\left(x+4\right)\)
\(=8x^2+12x-8x^2-32x\)
=-20x
e: Ta có: \(2x\left(5x+2\right)+\left(2x-3\right)\left(3x-1\right)\)
\(=10x^2+4x+6x^2-2x-9x+3\)
\(=16x^2-7x+3\)
f: Ta có: \(x\left(x+2\right)^2-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(=x^3+4x^2+4x-x^3-3x^2-3x-1+3x^2-3\)
\(=4x^2+x-4\)
\(a.\) \(ax^2-a^2x-x+a\)
\(=\left(ax^2-a^2x\right)-\left(x-a\right)\)
\(=ax\left(x-a\right)-\left(x-a\right)\)
\(=\left(ax-1\right)\left(x-a\right)\)
\(b.\) \(18x^3-12x^2+2x\)
\(=2x\left(9x^2-6x+1\right)\)
\(=2x\left(3x-1\right)^2\)
\(c.\) \(x^3-5x^2-4x+20\)
\(=\left(x^3-5x^2\right)-\left(4x-20\right)\)
\(=x^2\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x^2-4\right)\left(x-5\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-5\right)\)
\(d.\) \(\left(x+7\right)\left(x+15\right)+15\)
\(=x^2+15x+7x+105+15\)
\(=x^2+22x+120\)
\(=\left(x+10\right)\left(x+12\right)\)
a: \(=\left(2x^2-x\right)^2-5\left(2x^2-x\right)-6\)
\(=\left(2x^2-x\right)^2-6\left(2x^2-x\right)+\left(2x^2-x-6\right)\)
\(=\left(2x^2-x-6\right)\left(2x^2-x+1\right)\)
\(=\left(2x^2-4x+3x-6\right)\left(2x^2-x+1\right)\)
\(=\left(x-2\right)\left(2x+3\right)\left(2x^2-x+1\right)\)
b: \(=\left(5x^2-2x\right)^2-\left(5x^2-2x\right)-6\)
\(=\left(5x^2-2x-6\right)\left(5x^2-2x+1\right)\)
d: \(=\left(x+2\right)\left(x-1\right)\left(x+3\right)\left(x+6\right)-28\)
\(=\left(x^2+5x+6\right)\left(x^2+5x-6\right)-28\)
\(=\left(x^2+5x\right)^2-36-28\)
\(=\left(x^2+5x\right)^2-64\)
\(=\left(x^2+5x+8\right)\left(x^2+5x-8\right)\)