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Bài 1:
a) \(\dfrac{15xy}{10x^2y}\)
= \(\dfrac{3.5xy}{2.5xyx}\)
= \(\dfrac{3}{2x}\)
d) \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)
= \(\dfrac{3.2x\left(x+5\right)\left(x+5\right)^2}{x.2x\left(x+5\right)}\)
= \(\dfrac{3\left(x+5\right)^2}{x}\)
a) 6x2.(3x2 - 4x + 5) = 18x4 - 24x3 + 30x2
b) (x - 2y)(3xy + 6y2 + x) = 3x2y + 6xy2 + x2 - 6xy2 - 12y3 - 2xy = -12y3 + 3x2y - 2xy + x2
c) (18x4y3 - 24x3y4 + 12x3y3) : (-6x2y3) = -6x2y3(-3x2 + 4xy - 2x) : (-6x2y3) = 4xy - 3x2 - 2x
a) \(5x\left(3x-7\right)-15x\left(x-1\right)=3\)
\(\Rightarrow15x^2-35x-15x^2+15x=3\)
\(\Rightarrow-20x=3\)
\(\Rightarrow x=-\dfrac{3}{20}\)
b) \(\left(4x+2\right)\left(6x-3\right)-\left(8x+5\right)\left(3x-4\right)=2\)
\(\Rightarrow24x^2+12x-12x-6-24x^2-15x+24x+20=2\)
\(\Rightarrow9x+14=2\)
\(\Rightarrow9x=-12\)
\(\Rightarrow x=-\dfrac{4}{3}\)
c) \(7x^2-21x=0\)
\(\Rightarrow7x\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}7x=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
d) \(9x^2-6x+1=0\)
\(\Rightarrow\left(3x\right)^2-2.3x+1=0\)
\(\Rightarrow\left(3x-1\right)^2=0\)
\(\Rightarrow3x-1=0\)
\(\Rightarrow3x=1\)
\(\Rightarrow x=\dfrac{1}{3}\)
e) \(16x^2-49=0\)
\(\Rightarrow\left(4x\right)^2-7^2=0\)
\(\Rightarrow\left(4x-7\right)\left(4x+7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}4x-7=0\\4x+7=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}4x=7\\4x=-7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{4}\\x=-\dfrac{7}{4}\end{matrix}\right.\)
f) \(5x^3-20x=0\)
\(\Rightarrow5x\left(x^2-4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}5x=0\\x^2-4=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x^2=4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=2\\x=-2\end{matrix}\right.\)
\(x^6-x^4-9x^3+9x^2\)
\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)
\(=x^4\left(x+1\right)\left(x-1\right)-9x^2\left(x-1\right)\)
\(=\left(x^5+x^4\right)\left(x-1\right)-9x^2\left(x-1\right)\)
\(=\left(x-1\right)\left(x^5+x^4-9x^2\right)\)
\(x^4+x^3+6x^2+5x+5\)
\(=x^4+x^3+x^2+5x^2+5x+5\)
\(=x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)\)
\(=\left(x^2+5\right)\left(x^2+x+1\right)\)
\(\left(12x^2-12xy+3y^2\right)-10\left(2x-y\right)+8\)
\(=3\left(4x^2-4xy+y^2\right)-10\left(2x-y\right)+8\)
\(=3\left[\left(2x\right)^2-2.2x.y+y^2\right]-10\left(2x-y\right)+8\)
\(=3\left(2x-y\right)^2-10\left(2x-y\right)+8\)
\(=\left(2x-y\right)\left[3\left(2x-y\right)-10\right]+8\)
\(=\left(2x-y\right)\left(6x-3y-10\right)+8\)
a)\(\dfrac{12x^3y^2}{18xy^5}\)=\(\dfrac{2x^2}{3y^3}\)
b)\(\dfrac{15x.\left(x+5\right)^2}{20x^2.\left(x+5\right)}\)=\(\dfrac{3.5x\left(x+5\right)}{4x.5x.\left(x+5\right)}\)=\(\dfrac{3\left(x+5\right)}{4x}\)
a) M.( -2x^2) = ( -15x^4y^6 - 20x^3y^5 +25x^4y^4)
M = (-15x^4y^6 - 20x^3y^5 +25x^4y^4) : (-2x^2)
M =7,5x^2y^6+10xy^5 - 12,5x^2y^4
b) M.( - 2x^2) = (3x^5 - 4x^4 +6x^3 )
M = (3x^5 - 4x^4 + 6x^3) : ( - 2x^2)
M = - 1,5x^3 +2x^2 - 3x
a: \(=3y^2-5x^2y^3-2y^2+3x^2y^3=y^2-2x^2y^3\)
b: \(=6x-y+2x^2+3y^2-2x^2+x=7x-y+3y^2\)
c: \(=x-y+4y^2-6xy+\dfrac{10x^2}{y}\)
1, = \(\dfrac{-5x^4}{3}\)
2, = \(\dfrac{-2xy}{3}\)
\(20x^5\div\left(-12x\right)=\dfrac{-5}{3}x^4\)