Question

Factor: 4b^3 - 12b^2 - 9b + 27

Answer 1

Answer:

(2b - 3)(2b + 3)(b - 3)

Step-by-step explanation:

4b³ - 9b - 12b² + 27

b(4b² - 9) - 3(4b² - 9)

(4b² - 9)(b - 3)

(2b - 3)(2b + 3)(b - 3)

Answer 2

Answer:

$(4b^{2}-9)(b-3)$

Step-by-step explanation:

In order to factor this expression you need to factor by grouping.

First focus on factoring the first two terms them factor the last two terms

1. Lets focus on the first 2 terms:

$4b^{3} -12b^{2}$ (You can factor out $4b^{2}$)

$4b^{2} (b-3)$ (this is what you're left with

2. Lets focus on the last 2 terms:

$-9b+27$ (You can factor our a -9)

$-9(b-3)$ (this is what you're left with

3. Now lets put both of the factored parts together:

$4b^{2} (b-3)-9(b-3)$ (Since both equations have the factor (b-3) in common that is one of our answers) (pull out that factor)

$(b-3)$

Now whatever is left create the second factor:

$(4b^{2} -9)$

So, $(4b^{2} -9)(b-3)$ are the factors that make this expression.

You can double check that these are the right factors by using the FOIL method.

If you use the FOIL method it forms the original expression $4b^{3} -12b^{2} -9b+27$

so we know for sure these are the right factors.

I will upload an image of how to use the FOIL method.

FOIL stand for Front, Outer, Inner, Last