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

##### 2 Answers

#### Answer:

First, extract a common factor.

#### Explanation:

2a(

Now you can factor the interior of the parentheses as a difference of squares.

.

2a(

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

2a(

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

Hopefully this helps!

#### Answer:

#### Explanation:

- 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)#