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Mình làm 1 bài thôi nhé
Bài 5
\(a.1-2y+y^2=\left(1-y\right)^2\)
\(b.\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x-4\right)\left(x+6\right)\)
\(c.1-4x^2=1-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
\(d.27+27x+9x^2+x^3=3^3+3.3^3.x+3.3.x^2+x^3=\left(3+x\right)^3\)
\(f.8x^3-12x^2y+6xy-y^3=\left(2x\right)^3-3.\left(2x\right)^2.y+3.2x.y-y^3=\left(2x-y\right)^3\)
Bài 4 :
a, \(x^3+3x^2-x-3=x^2\left(x+3\right)-\left(x+3\right)=\left(x+1\right)\left(x-1\right)\left(x+3\right)\)
b, bạn xem lại đề nhé
c, \(x^2-4x+4-y^2=\left(x-2\right)^2-y^2=\left(x-2-y\right)\left(x-2+y\right)\)
d, \(5x+5-x^2+1=5\left(x+1\right)+\left(1-x\right)\left(x+1\right)=\left(x+1\right)\left(6-x\right)\)
Bài 4 :
\(M=\left(2x-3y\right)^2-\left(3y-2\right)\left(3y+2\right)-\left(1-2x\right)^2+4x\left(3y-1\right)\)
\(=\left(2x-3y-1+2x\right)\left(2x-3y+1-2x\right)-9y^2+4+12xy-4x\)
\(=\left(4x-3y-1\right)\left(1-3y\right)-9y^2+4+12xy-4x\)
\(=4x-12xy-3y+9y^2-1+3y-9y^2+4+12xy-4x=3\)
Vậy biểu thức ko phụ thuộc giá trị biến x
Bài 2 :
a, \(\left(a-3b\right)^2=a^2-6ab+9b^2\)
b, \(x^2-16y^4=\left(x-4y^2\right)\left(x+4y^2\right)\)
c, \(25a^2-\frac{1}{4}b^2=\left(5a-\frac{1}{2}b\right)\left(5a+\frac{1}{2}b\right)\)
Bài 3 :
a, \(9x^2-6x+1=\left(3x-1\right)^2\)
b, \(\left(2x+3y\right)^2+2\left(2x+3y\right)+1=\left(2x+3y+1\right)^2\)
c, \(4\left(2x-y\right)^2-8x+4y+1=\left(4x-2y\right)^2-2\left(4x-2y\right)+1=\left(4x-2y-1\right)^2\)
a;b tìm nhân tử chung ở mẫu bạn tự làm nhé
c, \(\frac{3}{1-4x}=\frac{2}{4x+1}-\frac{8+6x}{16x^2-1}\)ĐK : \(x\ne\pm\frac{1}{4}\)
\(\Leftrightarrow-\frac{3}{4x-1}=\frac{2}{4x+1}-\frac{8+6x}{\left(4x-1\right)\left(4x+1\right)}\)
\(\Leftrightarrow-\frac{3\left(4x+1\right)}{\left(4x-1\right)\left(4x+1\right)}=\frac{2\left(4x-1\right)-8-6x}{\left(4x+1\right)\left(4x-1\right)}\)
\(\Rightarrow-12x-3=8x-2-8-6x\Leftrightarrow-14x=-7\Leftrightarrow x=\frac{1}{2}\)
i, \(\frac{x+2}{x+3}-\frac{x+1}{x-1}=\frac{4}{x^2+2x-3}\)ĐK : \(x\ne-3;1\)
\(\Leftrightarrow\frac{\left(x+2\right)\left(x-1\right)-\left(x+1\right)\left(x+3\right)}{\left(x+3\right)\left(x-1\right)}=\frac{4}{\left(x+3\right)\left(x-1\right)}\)
\(\Rightarrow x^2+x-2-x^2-4x-3=4\Leftrightarrow-3x-5=4\Leftrightarrow x=-3\)(ktm)
Vậy pt vô nghiệm
g, \(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)ĐK : \(x\ne1\)
\(\Leftrightarrow\frac{x^2+x+1+2x^2-5}{x^3-1}=\frac{4\left(x-1\right)}{x^3-1}\)
\(\Rightarrow3x^2+x-4=4x-4\Leftrightarrow3x^2-3x=0\Leftrightarrow x=0\left(tm\right);x=1\left(ktm\right)\)
h, \(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(5x-3\right)}\)ĐK : \(x\ne\frac{1}{5};\frac{3}{5}\)
\(\Leftrightarrow\frac{3\left(5x-3\right)-2\left(5x-1\right)}{\left(5x-1\right)\left(5x-3\right)}=\frac{-4}{\left(5x-1\right)\left(5x-3\right)}\)
\(\Rightarrow15x-9-10x+2=-4\Leftrightarrow5x=3\Leftrightarrow x=\frac{3}{5}\)(ktm)
Vậy pt vô nghiệm