Factor completely 200-2y to the fourth power?

Question

help please

thx

Answer 1

I'm going to assume you mean, instead,

200 - 2y⁴

You can factor out the 2, first:

2(100 - y⁴)

Then this is the difference of two squares:

2(10 - y²)(10 + y²)

Then the second term can be factored again as the difference of two squares:

2(√10 - y)(√10 + y)(10 + y²)

And that's as far as you can go.....


.....unless you also know about complex numbers, in which case, you can also factor the last term:

2(√10 - y)(√10 + y)(i√10 - y)(i√10 + y)

so the factors are √10, -√10, i√10, and -i√10.

Answer 2

I assume you mean (200 - 2y)^4; in other words, the exponent 4 applies to the whole expression 200 - 2y.
Well, 2 goes into both 2 and 200, so you can factor 200 - 2y as 2(100 - y). Raising that whole thing to the fourth power gives you (2^4)(100 - y)^4, which is 16(100 - y)^4.
That's about all I can think of to do to it!