Câu 1 : Thực hiện phép tính :
a) \(6x^2\left(3x^2-4x+5\right)\)
b) \(\left(3x-y\right)^2\)
c) \(\left(x+3\right)\left(x-3\right)-x\left(x-5\right)\)
d) \(\left(x+2\right)^2+\left(x-3y\right)^2-\left(2x+4\right)\left(x-3\right)\)
Câu 2 : Phân tích đa thức :
a) \(14x^2y-21xy^2+28x^2y^2\)
b) \(27x^3-\dfrac{1}{27}\)
c) \(3x^2-3xy-5x+5y\)
d) \(x^2+7x+12\)
Câu 3 : Tìm x :
a) \(5x\left(x-2\right)+3x-6=0\)
b) \(x^3=9x\)
c) \(\left(x+2\right)\left(x-2\right)=x\left(x-1\right)\)
Bài 1:
a, \(6x^2\left(3x^2-4x+5\right)=18x^4-24x^3+30x^2\)
b, \(\left(3x-y\right)^2=9x^2-6xy+y^2\)
c, \(\left(x+3\right)\left(x-3\right)-x\left(x-5\right)=x^2-9-x^2+5=-4\)
d, \(\left(x+2\right)^2+\left(x-3y\right)^2-\left(2x+4\right)\left(x-3\right)\)
\(=x^2+4x+4+x^2-6xy+9y^2-2x^2+2x+12\)
\(=9y^2+6x+16\)
Bài 2:
a, \(14x^2y-21xy^2+28x^2y^2=7xy\left(2x-3y+4xy\right)\)
b, \(27x^3-\dfrac{1}{27}=\left(3x\right)^3-\left(\dfrac{1}{3}\right)^3=\left(3x-\dfrac{1}{3}\right)\left(9x^2-x+\dfrac{1}{9}\right)\)
c, \(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
d, \(x^2+7x+12=x^2+3x+4x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)
Bài 3:
a, \(5x\left(x-2\right)+3x-6=0\Leftrightarrow5x\left(x-2\right)+3\left(x-2\right)=0\)
\(\Leftrightarrow\left(5x+3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+3=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-3}{5}\\x=2\end{matrix}\right.\)
b, \(x^3=9x\Leftrightarrow x^3-9x=0\Leftrightarrow x\left(x^2-9\right)=0\)
\(\Leftrightarrow x\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\)
c, \(\left(x+2\right)\left(x-2\right)=x\left(x-1\right)\Leftrightarrow\left(x+2\right)\left(x-2\right)-x\left(x-1\right)=0\)
\(\Leftrightarrow x^2-4-x^2+x=0\Leftrightarrow x-4=0\)
\(\Leftrightarrow x=4\)
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