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a)\(ax-2x-a^2+2a\)
\(=\left(ax-2x\right)-\left(a^2-2a\right)\)
\(=x\left(a-2\right)-a\left(a-2\right)\)
\(=\left(x-a\right)\left(a-2\right)\)
b)\(x^2+x-ax-a\)
\(=\left(x^2+x\right)-\left(ax+a\right)\)
\(=x\left(x+1\right)-a\left(x+1\right)\)
\(=\left(x-a\right)\left(x+1\right)\)
c)\(2x^2+4ax+x+2a\)
\(=\left(2x^2+4ax\right)+\left(x+2a\right)\)
\(=2x\left(x+2a\right)+\left(x+2a\right)\)
\(=\left(2x+1\right)\left(x+2a\right)\)
d)\(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)^2\)
\(=\left(x-y\right)\left(3\left(x+y\right)-2\left(x-y\right)\right)\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)

đề thiếu nha
a) ta có : \(\dfrac{2x^2+ax-4}{x+4}\in Z\Leftrightarrow2x^2+ax-4=\left(x+4\right)\left(2x+b\right)\)
\(\Leftrightarrow x^2+ax-4=2x^2+\left(b+8\right)x+4b\) \(\Rightarrow4b=-4\Leftrightarrow b=-1\)
\(\Rightarrow a=b+8=-1+8=7\) vậy \(a=7\)
câu kia lm tương tự nha bn

x\(^2\)-(a+b)x+ab
= x\(^2\)-ax-bx+ab
= x(x-a) - b(x-a)
= ( x-a).( x-b)
ax-2x-a\(^2\)+2a
= x(a-2) - a(a-2)
= (a-2).( x-a)

\(x^2-ax+2a-b⋮x^2+2x+1\)
nên \(\left\{{}\begin{matrix}-a=2\\2a-b=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-2\\b=2a-1=-5\end{matrix}\right.\)

a: \(=\dfrac{a}{9\left(a-2\right)}-\dfrac{b-1}{6b}-\dfrac{ab-3a+6}{9b\left(a-2\right)}\)
\(=\dfrac{2ab}{18b\left(a-2\right)}-\dfrac{3\left(b-1\right)\left(a-2\right)}{18b\left(a-2\right)}-\dfrac{2ab-6a+12}{18b\left(a-2\right)}\)
\(=\dfrac{2ab-3\left(ba-2b-a+2\right)-2ab+6a-12}{18b\left(a-2\right)}\)
\(=\dfrac{6a-12-3ab+6b+3a-6}{18b\left(a-2\right)}\)
\(=\dfrac{3a+12b-3ab-18}{18b\left(a-2\right)}\)
\(=\dfrac{a+4b-ab-6}{6b\left(a-2\right)}\)
b: \(=\dfrac{xa-2x+ax+a-x\left(a-2\right)}{a\left(a-2\right)}\)
\(=\dfrac{2ax-2x+a-xa+2x}{a\left(a-2\right)}=\dfrac{xa+a}{a\left(a-2\right)}=\dfrac{x+1}{a-2}\)
\(ax-2x-a^2+a+2a\) \(=x\left(a-2\right)-a^2+3a\)