Bài 7:
a) \(4a^3b-12a^2b^2+8ab^3\)
\(=4ab\left(a^2-3ab+2b^2\right)\)
\(=4ab\left(a^2-ab-2ab+2b^2\right)\)
\(=4ab\left(a-b\right)\left(a-2b\right)\)
b) \(\dfrac{5}{4}x^4+\dfrac{3}{4}x^3-\dfrac{1}{5}x^2\)
\(=x^2\cdot\left(\dfrac{5}{4}x^2+\dfrac{3}{4}x-\dfrac{1}{5}\right)\)
\(=x^2\cdot\dfrac{1}{4}\cdot\left(5x^2+3x-\dfrac{4}{5}\right)\)
\(=\dfrac{x^2}{4}\cdot\left(5x^2+3x-\dfrac{4}{5}\right)\)
c) \(3x^2\left(x+9\right)-2\left(x+9\right)\)
\(=\left(x+9\right)\left(3x^2-2\right)\)
d) \(3x^2\left(7x+y\right)-5x\left(7x+y\right)+14x+2y\)
\(=3x^2\left(7x+y\right)-5x\left(7x+y\right)+2\left(7x+y\right)\)
\(=\left(7x+y\right)\left(3x^2-5x+2\right)\)
\(=\left(7x+y\right)\left(3x^2-3x-2x-2\right)\)
\(=\left(7x+y\right)\left(3x-2\right)\left(x-1\right)\)
Bài 8:
a: \(x^2-25x=0\)
=>\(x\left(x-25\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-25=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=25\end{matrix}\right.\)
b: \(7x\left(x-3\right)-5\left(3-x\right)=0\)
=>\(7x\left(x-3\right)+5\left(x-3\right)=0\)
=>\(\left(x-3\right)\left(7x+5\right)=0\)
=>\(\left[{}\begin{matrix}x-3=0\\7x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{7}\end{matrix}\right.\)
c: \(7x\left(x+4\right)-7x-28=0\)
=>\(7x\left(x+4\right)-7\left(x+4\right)=0\)
=>\(x\left(x+4\right)-\left(x+4\right)=0\)
=>\(\left(x+4\right)\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
d: \(\left(2x^2+5x\right)\left(x^2-x\right)+\left(2x^2+10\right)\left(x-x^2\right)=0\)
=>\(\left(2x^2+5x\right)\left(x^2-x\right)-\left(2x^2+10\right)\left(x^2-x\right)=0\)
=>\(\left(x^2-x\right)\left(2x^2+5x-2x^2-10\right)=0\)
=>\(5\left(x-2\right)\cdot x\left(x-1\right)=0\)
=>\(x\left(x-1\right)\left(x-2\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=2\end{matrix}\right.\)
