Question

Factor the polynomial. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. 27y^3-8 this factors into:(Answer - Answer)(Answer+Answer+Answer)

Answer 1

Since the terms in the polynomial 27y³ - 8 are both perfect cubes, then we can use the Difference of Cubes Formula which is:

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

Since the terms in our polynomial are perfect cubes, we can rewrite the equation into:

$(3y)^3-(2)^3$

in which a = 3y and b = 2. Therefore, the factors of the polynomial are:

$\begin{gathered} (a-b)(a^2+ab+b^2) \\ (3y-2)\lbrack(3y)^2+(3y)(2)+(2)^2\rbrack \\ (3y-2)(9y^2+6y+4) \end{gathered}$

The factors are (3y - 2) and (9y² + 6y + 4).