How do you factor the expression #2a ^5 - 32ab ^8#?

2 Answers
Jan 29, 2016

Answer:

First, extract a common factor.

Explanation:

2a(#a^4 - 16b^8#)

Now you can factor the interior of the parentheses as a difference of squares.
.
2a(#a^2 - 4b^4)(a^2 + 4b^4#)

As you can see, we can do another difference of squares.

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

This is fully factored, since we can simplify it no more.

Hopefully this helps!

Jan 29, 2016

Answer:

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

Explanation:

  1. common factor in the 2 terms ? yes 2a

expression is :# 2a( a^4 - 16b^8) #

Note: difference of squares # a^2 - b^2 = (a - b)( a + b )#

now. # a^4 - 16b^8 color(black)( " is a difference of squares")#

where # a = a^2 , b = 4b^4 #

so # a^4 - 16b^8 = (a^2 - 4b^4)(a^2 + 4b^4) #

Note now that #(a^2 - 4b^4) # is a difference of squares.

In the same way as above : #a^2 - 4b^4 = (a-2b^2)(a+ 2b^2) #

'Pull this together ' to get:

# 2a^5 - 32ab^8 = 2a(a-2b^2)(a+2b^2)(a^2+ 4b^4)#