Factoring Special Cases

The difference of cubes is a special case of factoring that applies to expressions of the form a^3 - b^3, which can be factored as (a - b)(a^2 + ab + b^2).

(4 - 3a)(9a^2 + 12a + 16)

The sum of cubes is a special case of factoring that applies to expressions of the form a^3 + b^3, which can be factored as (a + b)(a^2 - ab + b^2).

(7m + 2)(49m^2 - 14m + 4) (using the sum of cubes formula)

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

(3x + 2)(9x^2 - 6x + 4)

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

(5x - 4)(25x^2 + 20x + 16)

Identify if the expression is a special case (like difference or sum of cubes) or if it can be factored by grouping.

The coefficients in the factored form provide information about the roots of the polynomial and can help in graphing the function.