how would you factor this?

Question

please explain
hint- you have to use "trial and error"

162y^5 - 32y

and

x^4 - 50x^2 + 32y

sorry, the second one is

x^4 - 50x^2 + 625

Answer 1

PROBLEM 1:

First factor out a common 2y:

2y(81y^4 - 16)

Notice that the last part is a difference of squares:
2y((9y²)² - 4²)

Use the rule for difference of squares a² - b² = (a - b)(a + b)

2y(9y² - 4)(9y² + 4)

Now notice that you have another difference of squares in the first parentheses:
2y((3y)² - 2²)(9y² + 4)

Use the rule again:
2y(3y - 2)(3y + 2)(9y² + 4)

That's as far as you can go...

PROBLEM 2:

The best you can do here is to factor out a common x²:

x²(x² - 50) + 32y

Are you sure that was the correct question?

Answer 2

162y^5 - 32y
= 2y(81y^4 - 16)
= 2y((9y^2)^2 - 4^2)
= 2y(9y^2 + 4)(9y^2 - 4)
= 2y(9y^2 + 4)((3y)^2 - 2^2)
= 2y(9y^2 + 4)(3y + 2)(3y - 2).

x^4 - 50x^2 + 625
= (x^2)^2 - 50(x^2) + 625
= (x^2 - 25)^2
= (x^2 - 5^2)^2
= ((x + 5)(x - 5))^2
= (x + 5)^2 (x - 5)^2.

No trial & error.

Answer 3

162y^5 - 32y

= 2y(81y^4 - 16)

= 2y(9y^2 + 4)(9y^2 - 4)

= 2y(9y^2 + 4)(3y + 2)(3y - 2).

Are you sure you`ve copied the next one down correctly ?

Answer 4

Simplifying
162y^5 + -32y

Reorder the terms:
-32y + 162y^5

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-16 + 81y^4)

Factor a difference between two squares.
2y((4 + 9y^2)(-4 + 9y^2))

Factor a difference between two squares.
2y((4 + 9y^2)((2 + 3y)(-2 + 3y)))

Final result:
2y(4 + 9y^2)(2 + 3y)(-2 + 3y)





Simplifying
x^4 + -50x^2 + 32y

Reorder the terms:
-50x^2 + x^4 + 32y

Final result:
-50x^2 + x^4 + 32y

Answer 5

don't know about trial and error, but to factor, you take out the similarities. so out of the 162y... u take out a y from both things, and 2. so the answer is 4y(81y^4-16)

second one i have no idea how to factor. It's been a while since i've done factoring so there may be something i missed.... i think there is some way to take out square stuff but i can't remember