125.sagews

2.1. {3 {x}^{2} } + {5 x}+ {17 x}-{{x}^{2} }.

simplify(3*x^2+5*x +17*x-x^2)

{2 {x}^{2} } + {22 x}

2.2. {{\left( x - 1 \right)} {\left( x - 1 \right)} \left( {2 x} - 3 \right)}.

f=(x-1)*(x-1)*(2*x-3); simplify(f)

{{\left( x - 1 \right)}^{2} \left( {2 x} - 3 \right)}

f=(x-1)*(x-1)*(2*x-3); f.simplify()

{{\left( x - 1 \right)}^{2} \left( {2 x} - 3 \right)}

2.3. : {{\left( x - 1 \right)} \left( {x}^{2} - 1 \right)}.

expand((x-1)*(x^2-1))

{x}^{3} - {x}^{2} - x + 1

2.4. : {{3}{x}{\left( x - 6 \right)} -\left( {2}{x}^{2} - 14 \right)}.

a=3*x*(x-6)-(2*x^2-14); a

{-2 {x}^{2} } + {{3 \left( x - 6 \right)} x} + 14

expand(a)

{x}^{2} - {18 x} + 14

2.5. : {{\left( x - 1 \right)} \left( {x}^{2} - {2}{x} + 2 \right)}.

b=(x-1)*(x^2-2*x+2); b

{\left( x - 1 \right) \left( {x}^{2} - {2 x} + 2 \right)}

b.expand()

{x}^{3} - {3 {x}^{2} } + {4 x} - 2

2.6. {{x}^{12}-1}.

factor(x^12-1)

{{{{{\left( x - 1 \right) \left( x + 1 \right)} \left( {x}^{2} + 1 \right)} \left( {x}^{2} - x + 1 \right)} \left( {x}^{2} + x + 1 \right)} \left( {x}^{4} - {x}^{2} + 1 \right)}

2.7. {{a}^{2}-{ab}-{4a}+{4b}}.

var('a,b')
factor(a^2-a*b-4*a+4*b)

{\left( a - 4 \right) \left( a - b \right)}

2.8. {{ax}+{ay}-{az}+{nx}+{ny}-{nz}}.

var('x,y,z,a,n')

\left(x, y, z, a, n\right)

exp=a*x+a*y-a*z+n*x+n*y-n*z; exp

{-n z} - {a z} + {n y} + {a y} + {n x} + {a x}

factor(exp)

{\left( n + a \right) \left( -z + y + x \right)}

2.9. {\sqrt[3]{x}+{\frac{1}{8}}{\sin \left( {10 x} \right)}} {{x}={2}}.

f(x)=x^(1/3)+1/8*sin(10*x); f(x)

\frac{\sin \left( {10 x} \right)}{8} + {x}^{\frac{1}{3}}

f(2)

\frac{\sin \left( 20 \right)}{8} + {2}^{\frac{1}{3}}

RR(f(2))

1.37403920623583

2.10. {{a}^{2}-{ab}-{4a}+{4b}} {{b}={2}}.

g(a,b)=(a^2-a*b-4*a+4*b);g(a,b)

{-a b} + {4 b} + {a}^{2} - {4 a}

g(a,2)

{a}^{2} - {6 a} + 8