How do you factor w^4-625w4−625?

3 Answers
1s2s2p
Jun 18, 2018

(w^2+25)(w-5)(w+5)(w2+25)(w−5)(w+5)

Explanation:

625=5^4625=54

w^4-5^4w4−54, using the difference of two squeares we get:

(w^2+5^2)(w^2-5^2)(w2+52)(w2−52)

And again:
(w^2+25)(w-5)(w+5)(w2+25)(w−5)(w+5)

smendyka
Jun 18, 2018

See a solution process below:

Explanation:

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

(w^2)^2 - (25)^2 => (w^2 + 25)(w^2 - 25)(w2)2−(25)2⇒(w2+25)(w2−25)

We can then factor the term on the right as:

(w^2 + 25)(w + 5)(w - 5)(w2+25)(w+5)(w−5)

Martin C.
Jun 18, 2018

(w+5)(w-5)(w^2+25)(w+5)(w−5)(w2+25)

Explanation:

Remember that a^2-b^2=(a+b)(a-b)a2−b2=(a+b)(a−b)

w^4-625w4−625
=(w^2)^2-25^2=(w2)2−252
=(w^2-25)(w^2+25)=(w2−25)(w2+25)
=(w^2-5^2)(w^2+25)=(w2−52)(w2+25)
=(w+5)(w-5)(w^2+25)=(w+5)(w−5)(w2+25)

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