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

1 Answer
Apr 18, 2016

Answer:

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

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 #b^4 = b^2xxb^2" and " 256 = 16xx16#

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) #