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\(4x^2+4x-3\)
\(4x^2+4x+1-4\)
\(\left(2x+1\right)^2-2^2\)
\(\left(2x+1-2\right)\left(2x+1+2\right)\)
\(\left(2x-1\right)\left(2x+3\right)\)
\(4x^4-8x^3+4x^3-8x^2+x^2-2x-2x+4\\ =4x^3\left(x-2\right)+4x^2\left(x-2\right)+x\left(x-2\right)-2\left(x-2\right)\\ =\left(x-2\right)\left(4x^3+4x^2+x-2\right)\\ =\left(x-2\right)\left(4x^3-2x^2+6x^2-3x+4x-2\right)\\ =\left(x-2\right)\left[2x^2\left(2x-1\right)+3x\left(2x-1\right)+2\left(2x-1\right)\right]\\ =\left(x-2\right)\left(2x-1\right)\left(2x^2+3x-2\right)\)
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
\(x^3+4x^2+4x+1\)
\(=x^3+3x^2+x+x^2+3x+1\)
\(=x\left(x^2+3x+1\right)+\left(x^2+3x+1\right)\)
\(=\left(x+1\right)\left(x^2+3x+1\right)\)
\(4x^4+4x^3-x^2-x\)
\(=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=\left(x+1\right)\left(4x^3-x\right)\)
\(=x\left(x+1\right)\left(4x^2-1\right)\)
\(=x\left(x+1\right)\left[\left(2x\right)^2-1\right]\)
\(=x\left(x+1\right)\left(2x+1\right)\left(2x-1\right)\)
(Nhớ k cho mình với nhá!)
\(4x^2+4x-3=\left(2x\right)^2+2.\left(2x\right).1+1^2-4=\left(2x+1\right)^2-2^2=\left(2x+1-2\right)\left(2x+1+2\right)=\left(2x-1\right)\left(2x+3\right)\)
\(x^4+4x^3+2x^2-4x+1\)
\(=x^4+2x^3-x^2+2x^3+4x^2-2x-x^2-2x+1\)
\(=x^2\left(x^2+2x-1\right)+2x\left(x^2+2x-1\right)-\left(x^2+2x-1\right)\)
\(=\left(x^2+2x-1\right)^2\)
4x2+4x-3
= 4x2+4x+1-4
=(2x+1)2-22
=(2x+1-2)(2x+1+2)
=(2x-1)(2x+3)
\(4x^2+4x-3\)
\(= 4x^2 + 4x + 1 -4\)
\(= ( 2x+1)^2 -2^2\)
\(= (2x+1-2)(2x+1+2)\)
\(= (2x-1)(2x+3)\)