# How do you factor completely #4b^4-1024#?

##### 1 Answer

Apr 18, 2016

#### Explanation:

The first step is to take out the common factor of 4.

#rArr 4(b^4 - 256) # now

#(b^4 - 256)" is a difference of squares " #

since

a difference of squares factors as follows

#color(red)(|bar(ul(color(white)(a/a)color(black)( a^2 - b^2 = (a - b)(a + b))color(white)(a/a)|)))# here a

#= b^2" and b = 16 #

#rArr b^4 - 256 = (b^2 - 16)(b^2 + 16) # now

#b^2 - 16" is also a difference of squares " # and factors as

# (b - 4)(b + 4) # Putting this together gives

#4b^4 - 1024 = 4(b^2 +16)(b - 4)(b + 4) #