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a) \(=\left(x-2y\right)\left(x^2+5x\right)\)
b) \(=\left(x-1\right)\left(x^2+2x+1\right)=\left(x-1\right)\left(x+1\right)^2\)
c) \(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(3-x+3\right)\)
\(=\left(x+3\right)\left(6-x\right)\)
e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)
f) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
a,x4-4x3+8x2-16x+16
=(x4-4x3+4x2)+(4x2-16x+16)
=(x^2-2x)^2+(2x-4)^2
=x^2(x-2)^2+4(x-2)^2
=(x-2)^2(x^2+4)
a,x4-4x3+8x2-16x+16
=x4-4x3+4x2+4x2-16x+16
=x2.(x-2)2+4.(x-2)2
=(x-2)2(x2+4)
a,X^3-16x =x(x^2-16)
b,y(y-2)-3(y-2)=(y+3).(y-2)
c,x^2+4x+4-y^2=(x+2)^2-y^2=(x+y+2).(x+2-Y)
D,4^2y^3-12x^2y^4+16X^5y^3=4x^2y^2(y-3y^2+4X^3y)
x^4 - 4x^3 - 8x^2 - 16x + 16
= x^4-8x^2+16-4x^3-16x
= ( x^2+4)^2 - 4x(x^2+4 )
= ( x^2 + 4 )(x^2 + 4 - 4x)
= (x^2 + 4 )( x - 2 )^2
a) \(x^3-2x^2+x+xy^2\)
\(=x\left(x^2-2x+1+y^2\right)\)
\(=x\left[\left(x-1\right)^2+y^2\right]\)
\(=-x\left[\left(x-1\right)^2-y^2\right]\)
\(=-x\left(x-1+y\right)\left(x-1-y\right)\)
b) \(4x^2+16x+16\)
\(=4\left(x^2+4x+4\right)\)
\(=4\left(x+2\right)^2\)
\(x^2y-x^3-16y+16x=\left(x^2y-x^3\right)-\left(16y-16x\right)=x^2\left(y-x\right)-16\left(y-x\right)=\left(x^2-16\right)\left(y-x\right)=\left(x-4\right)\left(x+4\right)\left(y-x\right)\)
\(x^2y-x^3-16y+16x=-x^2\left(x-y\right)+16\left(x-y\right)=\left(x-y\right)\left(16-x^2\right)=\left(x-y\right)\left(4-x\right)\left(4+x\right)\)