# How do you factor #4m^3+9m^2-36m-81#?

##### 1 Answer

Nov 22, 2016

#### Explanation:

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We will use this with

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms, so this cubic will factor by grouping:

#4m^3+9m^2-36m-81 = (4m^3+9m^2)-(36m+81)#

#color(white)(4m^3+9m^2-36m-81) = m^2(4m+9)-9(4m+9)#

#color(white)(4m^3+9m^2-36m-81) = (m^2-9)(4m+9)#

#color(white)(4m^3+9m^2-36m-81) = (m^2-3^2)(4m+9)#

#color(white)(4m^3+9m^2-36m-81) = (m-3)(m+3)(4m+9)#