1a) \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)

b) \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)

\(a,=-\left(x-1\right)^3\left[=\left(1-x\right)^3\right]\\ b,=\left(1-x\right)^3\)

\(=\left(3x-y\right)\left(9x-3y\right)=3\left(3x-y\right)^2\)

=9x(3x-y)-3y(3x-y)
=(3x-y)(9x-3y)
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\(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)

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\(x^3-3x^2+3x-1-y^3\\ =\left(x-1\right)^3-y^3=\left(x-1-y\right)\left[\left(x-1\right)^2+y\left(x-1\right)+y^2\right]\\ =\left(x-y-1\right)\left(x^2-2x+1+xy-y+y^2\right)\)

\(x^3+3x^2+3x+1-y^3\\ =\left(x+1\right)^3-y^3=\left(x+1-y\right)\left[\left(x+1\right)^2+y\left(x+1\right)+y^2\right]\\ =\left(x-y+1\right)\left(x^2+2x+1+xy+y+y^2\right)\)

a/ \(4x^2-9\)

\(=\left(2x-3\right)\left(2x+3\right)\)

b/ \(3x\left(3x-2\right)+1\)

\(=9x^2-6x+1\)

\(=\left(3x-1\right)^2\)

\(a,=\left(2x-3\right)\left(2x+3\right)\)

\(b,=9x^2-6x+1=\left(3x-1\right)^2\)

= (x³+3x²+3x+1)-(4y)³

=(x+1)³-(4y)³

=(x+1-4y)[(x+1)²+(x+1).4y+16y² ]

=(x+1-4y)[(x²+2x+1)+(4xy+4y)+16y²]

\(=\left(x+3x-1\right)\left(x^2-3x^2-x+9x^2-6x+1\right)\)

\(=\left(4x-1\right)\left(7x^2-7x+1\right)\)

x3 + 3x2 + 3x + 1 = x3 + 3x2.1 + 3x.12 + 13 = (x + 1)3