\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+6y\right)\)
\(=2\left(x-y\right)\left(5x+3y\right)\)
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\(3x\left(x-2y\right)+6y\left(2y-x\right)\)
\(=3x\left(x-2y\right)-6y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(3x-6y\right)\)
\(=2\left(x-2y\right)^2\)
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\(20x\left(x+y\right)-8y\left(y+x\right)\)
\(=\left(x+y\right)\left(20x-8y\right)\)
\(=4\left(x+y\right)\left(5x-2y\right)\)
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\(xy^2\left(x-3\right)+4x\left(3-x\right)\)
\(=xy^2\left(x-3\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(xy^2-4x\right)\)
\(=x\left(x-3\right)\left(y^2-4\right)\)
\(=x\left(x-3\right)\left(y+2\right)\left(y-2\right)\)
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\(2x\left(x+y\right)-6x^2\left(x+y\right)\)
\(=\left(x+y\right)\left(2x-6x^2\right)\)
\(=2x\left(x+y\right)\left(1-3x\right)\)
____
\(9x^2\left(y+z\right)+3x\left(y+z\right)\)
\(=\left(y+z\right)\left(9x^2+3x\right)\)
\(=3x\left(y+z\right)\left(3x+1\right)\)
