How to use

Polynomial Expansion Animation

Expand polynomials one step at a time, with animated arrows.

The panel names in the top right open and close the Formula, Custom, Controls and How to Use panels. Pick an expression in the Formula panel, then step through it with the arrows in the Controls panel. Play runs it on its own, at slow, normal or fast speed.

One arrow is one multiplication. Every term of the first bracket is multiplied by every term of the second, so two terms each gives four arrows and three terms each gives nine.

Once all the products are on the line, terms underlined in the same color are like terms, and combining them gives the answer. Treating each term together with its sign is the single best way to avoid mistakes.

In the Custom panel, put non-zero integers from −9 to 9 into aa, bb, cc and dd of (ax+b)(cx+d)(ax+b)(cx+d) and watch your own expression expand.

Drag a panel by its header to put it wherever you like. Panels snap to each other and to the edges of the screen, and the four edges and four corners resize them. Double-click a panel title to switch how the panels are laid out: the fixed layout keeps a single panel in the top right.

Formulas

m(a+b)=ma+mbm(a+b) = ma + mb
(a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d) = ac + ad + bc + bd
(x+a)(x+b)=x2+(a+b)x+ab(x+a)(x+b) = x^2 + (a+b)x + ab
(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2
(ab)2=a22ab+b2(a-b)^2 = a^2 - 2ab + b^2
(a+b)(ab)=a2b2(a+b)(a-b) = a^2 - b^2
(ax+b)(cx+d)=acx2+(ad+bc)x+bd(ax+b)(cx+d) = acx^2 + (ad+bc)x + bd
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
(a+b)3=a3+3a2b+3ab2+b3(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
(a+b)(a2ab+b2)=a3+b3(a+b)(a^2 - ab + b^2) = a^3 + b^3