Question

how to factor 16x^4-625

Answer 1

Here's a hint: the difference of two squared quantities can be factored as follows:

\[a^2-b^2 = (a-b)(a+b)\]

Answer 2

You may be able to apply that rule more than once in this problem!

Answer 3

wait never mind I think I got it, would it be (2x^2-5)?

Answer 4

Well, let's make all the pieces match between

\[16x^4-625\]and\[a^2-b^2\]We'll set \[a^2=16x^4\]and \[b^2=625\]
What are the values of \(a\) and \(b\)?

Answer 5

a=2 and b=5 right?

Answer 6

a=4 and b=25

Answer 7

yes on \(b\), no on \(a\)

Answer 8

4x^2 is a

Answer 9

That's better :-)

Answer 10

so it would be (4x^2-25) (2x-5) (2x+5) right?

Answer 11

i mean +25

Answer 12

So, if \(a = 4x^2\) and \(b = 25\), we can rewrite our polynomial as
\[16x^4-625 = a^2-b^2 = (a-b)(a+b) = (4x^2-25)(4x^2+25)\]

Answer 13

Yes! You correctly spotted that one of the factors was also a difference of squares, great!

Answer 14

thank you!

Answer 15

There's also a formula for the difference of cubes, but it isn't quite so neat and tidy.

Answer 16

\[a^3-b^3 = (a-b)(a^2+ab+b^2)\]

Answer 17

umm idk

Answer 18

@tanzie32 what don't you know?