giup e aa
a: \(12x^5y^9+18x^4y^{12}-30x^{12}y^5\)
\(=6x^4y^5\cdot2xy^4+6x^4y^5\cdot3y^7-6x^4y^5\cdot5x^8\)
\(=6x^4y^5\left(2xy^4+3y^7-5x^8\right)\)
b: \(x^2+\dfrac{1}{2}xy+\dfrac{1}{16}y^2\)
\(=x^2+2\cdot x\cdot\dfrac{1}{4}y+\left(\dfrac{1}{4}y\right)^2\)
\(=\left(x+\dfrac{1}{4}y\right)^2\)
c: \(9x^2-3x+2y-4y^2\)
\(=\left(9x^2-4y^2\right)-\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(3x+2y\right)-\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(3x+2y-1\right)\)
d: \(x^3-y^3+3x^2+3x+1\)
\(=\left(x^3+3x^2+3x+1\right)-y^3\)
\(=\left(x+1\right)^3-y^3\)
\(=\left(x+1-y\right)\left[\left(x+1\right)^2+y\left(x+1\right)+y^2\right]\)
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