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27 tháng 10 2021
\(a,=8\left(x^2-2xy+y^2\right)=8\left(x-y\right)^2\\ b,=9\left(x^2-y^2\right)=9\left(x-y\right)\left(x+y\right)\\ c,=\left(x^2-y^2\right)-\left(9x+9y\right)\\ =\left(x-y\right)\left(x+y\right)-9\left(x+y\right)=\left(x+y\right)\left(x-y-9\right)\\ d,=3\left(x^2-4x+4-4y^2\right)=3\left[\left(x-2\right)^2-4y^2\right]\\ =3\left(x-2y-2\right)\left(x+2y-2\right)\\ e,=4x^2+4x+9x+9=4x\left(x+1\right)+9\left(x+1\right)\\ =\left(4x+9\right)\left(x+1\right)\\ f,Sai.đề\)
27 tháng 10 2021
a) \(8x^2-16xy+8y^2=8\left(x^2-2xy+y^2\right)=8\left(x-y\right)^2\)
b) \(9x^2-9y^2=9\left(x^2-y^2\right)=9\left(x-y\right)\left(x+y\right)\)
c) \(x^2-9x-9y-y^2=\left(x^2-y^2\right)-\left(9x+9y\right)=\left(x-y\right)\left(x+y\right)-9\left(x+y\right)=\left(x+y\right)\left(x-y-9\right)\)
d) \(3x^2-12x+12-12y^2=3\left(x^2-4x+4-4y^2\right)=3\left[\left(x-2\right)^2-4y^2\right]=3\left(x-2-4y\right)\left(x-2+4y\right)\)
e) \(4x^2+13x+9=\left(4x^2+4x\right)+\left(9x+9\right)=4x\left(x+1\right)+9\left(x+1\right)=\left(x+1\right)\left(4x+9\right)\)
11 tháng 2 2022
1.\(ĐK:x\ne\pm2\)
\(\Leftrightarrow\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}=\dfrac{4}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\dfrac{\left(x+2\right)\left(x+2\right)-\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{4}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow\left(x+2\right)^2-\left(x-2\right)^2=4\)
\(\Leftrightarrow x^2+4x+4-x^2+4x-4=4\)
\(\Leftrightarrow8x=4\)
\(\Leftrightarrow x=\dfrac{1}{2}\left(tm\right)\)
Vậy S = \(\dfrac{1}{2}\)
2.\(ĐK:x\ne1;-3\)
\(\Leftrightarrow\dfrac{x+1}{x-1}-\dfrac{x+2}{x+3}=-\dfrac{4}{\left(x-1\right)\left(x+3\right)}\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+3\right)-\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}=-\dfrac{4}{\left(x-1\right)\left(x+3\right)}\)
\(\Rightarrow x^2+3x+x+3-x^2+x-2x+2=-4\)
\(\Leftrightarrow3x=-9\)
\(\Leftrightarrow x=-3\left(ktm\right)\)
Vậy S vô nghiệm
11 tháng 2 2022
1) ĐKXĐ: \(x\ne\pm2\)
\(\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}=\dfrac{4}{x^2-4}\)
\(\Leftrightarrow\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}-\dfrac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{4}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow x^2+4x+4-x^2+4x-4=4\)
\(\Leftrightarrow8x=4\)
\(\Leftrightarrow x=\dfrac{1}{2}\left(tm\right)\)
Vậy ....
2) ĐKXĐ:\(x\ne1,-3\)
\(\dfrac{x+1}{x-1}-\dfrac{x+2}{x+3}+\dfrac{4}{x^2+2x-3}=0\)
\(\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\dfrac{\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}+\dfrac{4}{x^2-x+3x-3}=0\)
\(\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\dfrac{\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}+\dfrac{4}{\left(x-1\right)\left(x+3\right)}=0\)
\(\Rightarrow x^2+4x+3-x^2-x+2+4=0\)
\(\Leftrightarrow3x=-9\)
\(\Leftrightarrow x=-3\)(ktm)
NV
Nguyễn Việt Lâm
Giáo viên
21 tháng 12 2022
\(-2xy\left(4xy+9x^2+4y\right)=-2xy.4xy+\left(-2xy\right).9x^2+\left(-2xy\right).4y\)
\(=-8x^2y^2-18x^3y-8xy^2\)
\(x\left(x+8y\right)-y\left(8x-y^2\right)=x^2+8xy-8xy+y^3\)
\(=x^2+y^3\)
15 tháng 9 2021
1: \(100-x^2=\left(10-x\right)\left(10+x\right)\)
2: \(b^2-a^2=\left(b-a\right)\left(b+a\right)\)
3: \(\left(3y\right)^2-\left(4x\right)^2=\left(3y-4x\right)\left(3y+4x\right)\)
Cái này mình trước luôn nha: Mình sẽ tính diện tích 1 tam giác trước, rồi sau đó nhân cái đó với 2 là ra
\(S_{Tamgiác}=\dfrac{1}{2}\cdot6\cdot6\cdot sin30=9\left(cm^2\right)\)
\(S_{THOI}=9\cdot2=18\left(cm^2\right)\)