Explanation

Factorising by the Cross Method

Factorise quadratics one step at a time, with the cross method drawn out.

The panel names in the top right open and close the Topics, Examples and Explanation panels. Pick a quadratic in the Examples panel, then step through it with the arrows at the bottom of the screen. Drag the bar to jump to any moment, and the play button runs it on its own, at slow, normal or fast speed.

The cross method splits the x² coefficient down the left column and the constant term down the right column, so that each column multiplies back to the number it came from. Two numbers on the left, two on the right, and the two rows across are the factors you are looking for.

Then multiply across the diagonals and add the two products. If the sum is the x coefficient, the split was right and each row across becomes a factor. If it is not, the combination has to change, and the animation shows that retry rather than skipping to the answer.

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

ax2+bx+c=(px+q)(rx+s)ax^2 + bx + c = (px + q)(rx + s)
a=pr,c=qsa = pr, \quad c = qs
b=ps+qrb = ps + qr