Exercise algebra.manipulation.polynomial.expand

Description
expand an expression to polynomial normal form

Derivations

1.

5*(x+1)

⇒ algebra.equations.linear.distr-times

5*x+5

2.

-3*(x-3)

⇒ algebra.equations.linear.distr-times

-3*x+9

3.

(x-1)*7

⇒ algebra.equations.linear.distr-times

7*x-7

4.

4*(3-2*x)

⇒ algebra.equations.linear.distr-times

-8*x+12

5.

(x+1)*(x-3)

⇒ algebra.equations.linear.distr-times

x^2-2*x-3

6.

(x+1)*(1-x)

⇒ algebra.equations.linear.distr-times

-x^2+1

7.

x*(x-1)

⇒ algebra.equations.linear.distr-times

x^2-x

8.

3*(x-2)*2*x

⇒ algebra.equations.linear.distr-times

(3*x-6)*2*x

⇒ algebra.equations.linear.distr-times

6*x^2-12*x

9.

(x-1)^2

⇒ algebra.equations.quadratic.distr-square

x^2-2*x+1

10.

(x+1)^2

⇒ algebra.equations.quadratic.distr-square

x^2+2*x+1

11.

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

⇒ algebra.equations.quadratic.distr-square

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

⇒ algebra.equations.linear.distr-times

x^3-x^2-x+1

12.

(x+1)^3

⇒ algebra.equations.polynomial.def-power-nat

(x+1)*(x+1)*(x+1)

⇒ algebra.equations.linear.distr-times

(x^2+x+x+1)*(x+1)

⇒ algebra.equations.linear.distr-times

x^3+3*x^2+3*x+1

13.

(x-1)^3*x

⇒ algebra.equations.polynomial.def-power-nat

(x-1)*(x-1)*(x-1)*x

⇒ algebra.equations.linear.distr-times

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

⇒ algebra.equations.linear.distr-times

(x^3-x^2-x^2+x-x^2+x+x-1)*x

⇒ algebra.equations.linear.distr-times

x^4-3*x^3+3*x^2-x

14.

(x-1)*(x+3)*(x-5)

⇒ algebra.equations.linear.distr-times

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

⇒ algebra.equations.linear.distr-times

x^3-3*x^2-13*x+15

15.

x/2

⇒ algebra.equations.linear.no-div-con

1/2*x

16.

(x+1)/2

⇒ algebra.equations.linear.no-div-con

1/2*(x+1)

⇒ algebra.equations.linear.distr-times

1/2*x+1/2

17.

(x+1)/2+(x+2)/3

⇒ algebra.equations.linear.no-div-con

1/2*(x+1)+(x+2)/3

⇒ algebra.equations.linear.distr-times

1/2*x+1/2+(x+2)/3

⇒ algebra.equations.linear.no-div-con

1/2*x+1/2+1/3*(x+2)

⇒ algebra.equations.linear.distr-times

1/2*x+1/2+1/3*x+2/3

⇒ algebra.equations.linear.merge

5/6*x+7/6

18.

(x+1)/2*((x+2)/3)

⇒ algebra.equations.polynomial.fraction-product

(x+1)*(x+2)/6

⇒ algebra.equations.linear.distr-times

(x^2+3*x+2)/6

⇒ algebra.equations.linear.no-div-con

1/6*(x^2+3*x+2)

⇒ algebra.equations.linear.distr-times

1/6*x^2+1/2*x+1/3