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a: \(=3x^2-3y^2=3\left(x-y\right)\left(x+y\right)\)
b: \(=\left(4x^2-7x-50\right)^2-\left(16x^4+56x^3+49x^2\right)\)
\(=\left(4x^2-7x-50\right)^2-\left(4x^2+7x\right)^2\)
\(=\left(4x^2-7x-50-4x^2-7x\right)\left(4x^2-7x-50+4x^2+7x\right)\)
\(=\left(-14x-50\right)\left(8x^2-50\right)\)
\(=-4\left(7x+25\right)\left(2x-5\right)\left(2x+5\right)\)
d: \(=\left(x^2+y^2\right)^3-8x^3y^3\)
\(=\left(x^2+y^2-2xy\right)\left[x^4+2x^2y^2+y^4+2x^3y^2+2x^2y^3+4x^2y^2\right]\)
\(=\left(x-y\right)^2\cdot\left[x^4+y^4+6x^2y^2+2x^3y^2+2x^2y^3\right]\)
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a: \(=3x^2-3y^2=3\left(x-y\right)\left(x+y\right)\)
c: \(=\left(x^2-y^2\right)^2-10\left(x^2-y^2\right)+25-4\left(x^2y^2+4xy+4\right)\)
\(=\left(x^2-y^2-5\right)^2-4\left(xy+2\right)^2\)
\(=\left(x^2-y^2-5-2xy-4\right)\left(x^2-y^2-5+2xy+4\right)\)
\(=\left(x^2-y^2-2xy-9\right)\left(x^2+2xy-y^2-1\right)\)
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a) \(3x^2-2x\left(5+1,5x\right)+10x\)
\(=3x^2-10x-3x^2+10x=0\)
b) \(7x\left(4y-x\right)+4y\left(y-7x\right)-2\left(2y^2-3,5x\right)\)
\(=28xy-7x^2+4y^2-28xy-4y^2+7x\)
\(=-7x^2+7x\)
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a: \(=7x^3\left(1-2xy+3x^2y^2\right)\)
b: \(=x\left(x-y\right)+11\left(x-y\right)=\left(x-y\right)\left(x+11\right)\)
c: \(=4\left(x-3\right)\left(x+3\right)\)
d: \(=\left(x+3\right)^2-4y^2=\left(x+3+2y\right)\left(x+3-2y\right)\)
e: \(=xy\left(x+1\right)+z\left(x+1\right)=\left(x+1\right)\left(xy+z\right)\)
f: \(=\left(x-y\right)\left(x+y\right)-6\left(x-y\right)=\left(x-y\right)\left(x+y-6\right)\)
\(7x^2y-35xy=7xy\left(x-5\right)\)
\(x^2-y^2+4y-4=x^2-\left(y^2-4y+4\right)=x^2-\left(y-2\right)^2=\left(x-y+2\right)\left(x+y-2\right)\)