phân tích đa thức -> nhân tử:
1) a3-a2x-ay+xy
2) x2+5x-6
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b: \(x^2-2xy+y^2-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
d: \(x^2+4x+3=\left(x+3\right)\left(x+1\right)\)
\(1,\\ a,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\\ b,=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\\ c,=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\\ d,=x\left(x-2y\right)+t\left(x-2y\right)=\left(x+t\right)\left(x-2y\right)\\ 2,\\ \Rightarrow x^2-4x+4-x^2+9=6\\ \Rightarrow-4x=-7\Rightarrow x=\dfrac{7}{4}\\ 3,\\ a,x^2+2x+2=\left(x+1\right)^2+1\ge1>0\\ b,-x^2+4x-5=-\left(x-2\right)^2-1\le-1< 0\)
\(2\left(x+5\right)-x^2-5x\)
\(=2\left(x+5\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(2-x\right)\)
\(y^2-6y+9-z^2\)
\(=\left(y-3\right)^2-z^2\)
\(=\left(y-3-z\right)\left(y-3+z\right)\)
\(=a^2\left(a-x\right)-y^2\left(a-x\right)=\left(a-x\right)\left(a-y\right)\left(a+y\right)\left(D\right)\)
a 3 – a 2 x – ay + xy = ( a 3 – a 2 x) – (ay – xy)
= a 2 (a – x) – y(a – x) = (a – x)( a 2 – y)
\(1,\\ 12x^6y^3:4x^3y=3x^3y^2\\ \left(x+1\right)\left(x^2-x+1\right)=x^3+1\\ 2x^2y\left(x^2+3xy\right)=3x^4y+6x^3y^2\\ 2,\\ a,=2xy\left(2x+3y-4\right)\\ b,=\left(x-3\right)\left(x+y\right)\\ c,=\left(x-2\right)\left(x+2\right)+y\left(x-2\right)=\left(x+y+2\right)\left(x-2\right)\\ d,=x^2-2x-5x+10=\left(x-2\right)\left(x-5\right)\\ 3,\\ a,\Leftrightarrow x^2-x^2+2x=2\\ \Leftrightarrow2x=2\Leftrightarrow x=1\\ b,\Leftrightarrow\left(x-2\right)\left(x-2+1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
a) a3 - a2x - ay + xy
= a2( a - x ) - y( a - x )
= ( a - x )( a2 - y )
b) x2 + 5x - 6
= x2 - x + 6x - 6
= x( x - 1 ) + 6( x - 1 )
= ( x - 1 )( x + 6 )
1)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a-x\right)\left(a^2-y\right)\)
2)
\(=x^2+2x+3x+6\)
\(=x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(x+3\right)\)