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Ta có: \(4x^2-9y^2\\ =\left(2x\right)^2-\left(3y\right)^2\\ =\left(2x-3y\right)\left(2x+3y\right)\)
Vậy: Chọn D
\(\left(2x-2013\right)^3+\left(2013-3y\right)^3+\left(3y-2x\right)^3.\)
\(=\left(2x-2013+2013-3y\right)\left[\left(2x-2013\right)^2-\left(2x-2013\right).\left(2013-3y\right)+\left(2013-3y\right)^2\right]+\left(3y-2x\right)^3\)
\(=\left(2x-3y\right).\left(4x^2-8042x+2013^2-4026x+6xy+2013^2-6039y+2013^2-12078y+9y^2\right)+\left(3y-2x\right)^3.\)
\(=\left(2x-3y\right).\left(4x^2+9y^2-12078x-18117y+6xy+3.2013^2\right)-\left(2x-3y\right)^3.\)
\(=\left(2x-3y\right).\left[4x^2+9y^2-12078x-18117y+6xy+3.2013^2-\left(2x-3y\right)^2\right]\)
\(=\left(2x-3y\right).\left(4x^2+9y^2-12078x-18117y+6xy+3.2013^2-4x^2+12xy-9y^2\right).\)
\(=\left(2x-3y\right).\left(-12078x-18117y+18xy+3.2013^2\right).\)
\(=\left(2x-3y\right).9.\left(-1342x-2013y+2xy+1350723\right).\)
\(=9.\left(2x-3y\right).\left[\left(-1342x+2xy\right)+\left(1350723-2013y\right)\right]\)
\(=9.\left(2x-3y\right).\left[-2x\left(671-y\right)+2013\left(671-y\right)\right]\)
\(=9.\left(2x-3y\right).\left(-2x+2013\right)\left(671-y\right)\)
Câu 2:
\(=\dfrac{x^2\left(2x-5\right)+3\left(2x-5\right)}{2x-5}=x^2+3\)
Câu 3:
\(\Leftrightarrow2n^2-4n+5n-10+3⋮n-2\)
\(\Leftrightarrow n-2\in\left\{1;-1;3;-3\right\}\)
hay \(n\in\left\{3;1;5;-1\right\}\)
Ta có: \(\left(2x+3y\right)^2-2\left(2x+3y\right)\)
\(=\left(2x+3y\right)\left(2x+3y-2\right)\)
\(\left(2x+3y\right)^2+2\left(2x+3y\right)+1=\left[\left(2x+3y\right)+1\right]^2=\left(2x+3y+1\right)^2.\)
\(\left(2x+3y\right)^2+2\left(2x+3y\right)+1=\left(2x+3y+1\right)^2\)
\(P\times Q\)
\(=\left(2x+3y\right)\times\left(2x-3y\right)\)
\(=\left(2x\right)^2-\left(3y\right)^2\)
\(=4x^2-9y^2\)
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