Cube of a binomial

Statement

Expand the special product: $(2x-1)^3$

Solution

Apply the formula $(A-B)^3 = A^3 - 3A^2B + 3AB^2 - B^3$ with $A=2x$ and $B=1$: $(2x-1)^3 = (2x)^3 - 3(2x)^2(1) + 3(2x)(1)^2 - 1^3 = \boxed{8x^3 - 12x^2 + 6x - 1}$

Links

Topics: Literal calculus
Concepts: Cube of a binomial · Special products
Skills: Calculating · Using formulae
Exercise type: Evaluating expressions