How do you factor #w^4-625#?

Question

3696 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-18T13:14:46

#(w^2+25)(w-5)(w+5)#

#625=5^4#

#w^4-5^4#, using the difference of two squeares we get:

#(w^2+5^2)(w^2-5^2)#

And again:
#(w^2+25)(w-5)(w+5)#

Answer 2 · 2018-06-18T13:14:49

See a solution process below:

First, we can rewrite the expression and factor it as:

#(w^2)^2 - (25)^2 => (w^2 + 25)(w^2 - 25)#

We can then factor the term on the right as:

#(w^2 + 25)(w + 5)(w - 5)#

Answer 3 · 2018-06-18T13:15:47

#(w+5)(w-5)(w^2+25)#

Remember that #a^2-b^2=(a+b)(a-b)#

#w^4-625#
#=(w^2)^2-25^2#
#=(w^2-25)(w^2+25)#
#=(w^2-5^2)(w^2+25)#
#=(w+5)(w-5)(w^2+25)#