How do you factor #2c^2-32d^2#?

Question

1807 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-12T21:47:27

#2(c-4d)(c+4d)#

Worth remembering the standard form of #(a^2-b^2)=(a-b)(a+b)#

IT CROPS UP ALL OVER THE PLACE

We have a version of it in this question!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So we look for values that we can square

2 is a problem so lets try and 'sort of' move it out of the way

Factor out 2 giving:

#2(c^2-16d^2)#

Now we are getting somewhere. The 16 can be written as #4^2# and we are looking for squared values

Write as:

#2(c^2-(4d)^2)#

So using the standard form of #a^2-b^2=(a-b)(a+b)# we write:

#2(c^2-(4d)^2)" "=2(c-4d)(c+4d)#