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\(a,=x^2+x+4x+4=\left(x+1\right)\left(x+4\right)\\ b,=x^2+2x-3x-6=\left(x-3\right)\left(x+2\right)\\ c,=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\\ d,=3\left(x^2-2x+5x-10\right)=3\left(x-2\right)\left(x+5\right)\\ e,=-3x^2+6x-x+2=\left(x-2\right)\left(1-3x\right)\\ f,=x^2-x-6x+6=\left(x-1\right)\left(x-6\right)\\ h,=4\left(x^2-3x-6x+18\right)=4\left(x-3\right)\left(x-6\right)\\ i,=3\left(3x^2-3x-8x+5\right)=3\left(x-1\right)\left(3x-8\right)\\ k,=-\left(2x^2+x+4x+2\right)=-\left(2x+1\right)\left(x+2\right)\\ l,=x^2-2xy-5xy+10y^2=\left(x-2y\right)\left(x-5y\right)\\ m,=x^2-xy-2xy+2y^2=\left(x-y\right)\left(x-2y\right)\\ n,=x^2+xy-3xy-3y^2=\left(x+y\right)\left(x-3y\right)\)
Bài 6
\(a,ĐK:x\ne\pm5\\ b,P=\dfrac{x-5+2x+10-2x-10}{\left(x-5\right)\left(x+5\right)}=\dfrac{x-5}{\left(x-5\right)\left(x+5\right)}=\dfrac{1}{x+5}\\ c,P=-3\Leftrightarrow\dfrac{1}{x+5}=-3\Leftrightarrow-3\left(x+5\right)=1\Leftrightarrow x=-\dfrac{16}{3}\\ \Leftrightarrow Q=\left(3x-7\right)^2=\left[3\cdot\left(-\dfrac{16}{3}\right)-7\right]^2=529\)
Bài 7:
\(a,ĐK:x\ne\pm3\\ b,P=\dfrac{3x-9+x+3+18}{\left(x-3\right)\left(x+3\right)}=\dfrac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{4}{x-3}\\ b,P=4\Leftrightarrow4\left(x-3\right)=4\Leftrightarrow x=4\)
\(d,=\dfrac{3y}{5x\left(x-y\right)}\\ e,=\dfrac{5x\left(x+2\right)\left(2-x\right)}{4\left(x-2\right)\left(x+2\right)}=\dfrac{-5x}{4}\\ f,=\dfrac{3\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)\left(6-x\right)}=\dfrac{-3\left(x+6\right)}{2\left(x+5\right)}\\ g,=\dfrac{3xy\left(x-3y\right)\left(x+3y\right)}{2x^2y^2\left(x-3y\right)}=\dfrac{3\left(x+3y\right)}{2xy}\\ h,=\dfrac{45x^2y\left(x-y\right)\left(x+y\right)}{10xy\left(y-x\right)}=\dfrac{-9x\left(x+y\right)}{2}\\ i,=\dfrac{12\left(a-b\right)\left(a+b\right)\left(a^2+ab+b^2\right)}{3\left(a+b\right)\left(a-b\right)^2}=\dfrac{4\left(a^2+ab+b^2\right)}{a-b}\)
e: \(=\dfrac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\dfrac{-2\left(x-2\right)}{x+2}=\dfrac{-10}{4}=-\dfrac{5}{2}\)
\(\dfrac{x}{a}=\dfrac{m-\dfrac{x}{2}}{m}\)
\(\Rightarrow xm=a\left(m-\dfrac{x}{2}\right)\)
\(\Rightarrow xm=am-\dfrac{ax}{2}\)
\(\Rightarrow2xm=2am-ax\)
\(\Rightarrow2xm+ax=2am\)
\(\Rightarrow x\left(2m+a\right)=2am\)
\(\Rightarrow x=\dfrac{2am}{a+2m}\)
`A=(x^2-2)(x^2+x-1)-x(x^3+x^2-3x-2)`
`=x^4+x^3-x^2-2x^2-2x+2-x^4-x^3+3x^2+2x`
`=(x^4-x^4)+(x^3-x^3)+(3x^2-x^2-2x^2)+(2x-2x)+2`
`=2`
\(\left(x^2-2x+3\right)\left(\frac{1}{2x}-5\right)\)
\(=\frac{x^2}{2x}-5x^2-\frac{2x}{2x}+10x+\frac{3}{2x}-15\)
\(=\frac{x^2}{2x}-5x^2-16+10x+\frac{3}{2x}\)
\(=-5x^2+\frac{x^2}{2x}+\frac{20x^2}{2x}+\frac{3}{2x}-16\)
\(=-5x^2+\frac{x^2+20x+3}{2x}-16\)
học tốt
(x^2-2x+3)(1/2x-5)=1/2x^3-5x^2-x^2+10x+3/2x-15=1/2x^3-6x^2+11,5x-15
a) \(x^2+xy+x\)
\(=x\left(x+y+1\right)\)
Thay x=77, y=22
\(=77\left(77+22+1\right)\)
\(=77.100=7700\)
b) \(x\left(x-y\right)+y\left(y-x\right)\)
\(=\left(x-y\right)\left(x-y\right)\)
\(=\left(x-y\right)^2\)
Thay x=53, y=3
\(=\left(53-3\right)^2\)
\(=50^2=2500\)
c) \(x\left(x-1\right)-y\left(1-x\right)\)
\(=\left(x+y\right)\left(x-1\right)\)
Thay x=2021, y=2029
\(=\left(2021+2019\right)\left(2021-1\right)\)
\(=4040.2020\)
\(=8160800\)