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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: \(=\left(x^2+y^2\right)^3-8x^3y^3\)
\(=\left(x^2+y^2-2xy\right)\left[x^4+2x^2y^2+y^4+2x^3y^2+2x^2y^3+4x^2y^2\right]\)
\(=\left(x-y\right)^2\cdot\left[x^4+y^4+6x^2y^2+2x^3y^2+2x^2y^3\right]\)
a) 3x2 - 7x + 2
= 3x2 - 6x - x + 2
= (3x2 - 6x) - (x - 2)
= 3x (x - 2) - (x - 2)
= (3x - 1) (x - 2)
x6+3x4y2-8x3y3+3x2y4+y6= x6+3x4y2+3x2y4+y6-8x3y3=(x2+y2)3-(2xy)3
= (x2+y2-2xy)[(x2+y2)2+2xy(x2+y2)+(2xy)2]= (x-y)2(x4+6x2y2+y4+2x3y+2xy3)
(x2+y2-5)2-4x2y2-16xy-16=(x2+y2-5)2-(4x2y2+16xy+16)=(x2+y2-5)2-(2xy+4)2
=(x2+y2-5+2xy+4)(x2+y2-5-2xy-4)=(x2+2xy+y2-1)(x2-2xy+y2-9)=[(x+y)2-1][(x-y)2-32]=(x+y-1)(x+y+1)(x-y-3)(x-y+3)
x4+324=x4+36x2+324-36x2=(x2+18)2-(6x)2=(x2+18-6x)(x2+18+6x)
a: \(=3x^2-3y^2=3\left(x-y\right)\left(x+y\right)\)
c: \(=\left(x^2-y^2\right)^2-10\left(x^2-y^2\right)+25-4\left(x^2y^2+4xy+4\right)\)
\(=\left(x^2-y^2-5\right)^2-4\left(xy+2\right)^2\)
\(=\left(x^2-y^2-5-2xy-4\right)\left(x^2-y^2-5+2xy+4\right)\)
\(=\left(x^2-y^2-2xy-9\right)\left(x^2+2xy-y^2-1\right)\)