A cube with side length [math]\left(a+b\right)[/math] can be decomposed into:[br]- a cube of side length [math]a[/math][br]- a cube of side length [math]b[/math][br]- 3 congruent prisms with square base of side length [math]a[/math] and height [math]b[/math][br]- 3 congruent prisms with square base of side length [math]b[/math] and height [math]a[/math][br][br][br]Use the slider to decompose the cube into these parts.[br]Drag the point that defines the lengths of [math]a[/math] and [math]b[/math] to explore the dissection. [br]Right click and drag or use the predefined gestures for mobile devices to rotate 3D View.
Use the formula displayed in the app above to expand [math]\left(2a+3b\right)^3[/math].[br]If you don't remember the formula, how can you expand the binomial above?
[math]8a^3+36a^2b+54ab^2+27b^3[/math][br]For example, you can rewrite [math]\left(2a+3b\right)^3[/math] as [math]\left(2a+3b\right)^2\left(2a+3b\right)[/math]
If you expand [math]\left(-x+y^2\right)^3[/math], you get
This polynomial [math]\frac{8}{125}x^6y^3-\frac{6}{5}x^5y^4+\frac{15}{2}x^4y^5-\frac{125}{8}x^3y^6[/math] is equal to...