Question

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

Answer 1

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!

Answer 2

`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)`