guys how do u do u^4-3u^2-4 and 2u^2v-18uv+28v? these ones are extremly hard for me?

Answer 1

u^4-3u^2-4

OK so let v = u^2

then the equation becomes

v^2 - 3v - 4

and it factors into

(v-4)(v+1)

substituting u^2 = v into this

(u^2-4)(u^2+1)

We can factor this further

(u+2)(u-2)(u^2+1)

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2u^2v-18uv+28v

I'm interpreting the first term as (2u^2)*v

so factor out 2v

2v(u^2 - 9u + 14)

2v(u-7)(u-2)

Answer 2

u^4 - 3u^2 - 4 =
(u^2 - 4) (u^2 +1) =
(u + 2)(u - 2)(u^2 + 1)
Solutions
u = 2
u = -2
u = +/- i

2u^2v-18uv+28v =
2v(u^2 - 9u + 14) =
2v(u - 7)(u - 2)
Solutions:
v = 0
u = 7
u = 2

Answer 3

1st one: let x = u^2 and substitute

2nd one: are you saying 2u^(2v) as in 2 to the (2v)th power? or more like v*2u^2? If it's the latter, factor out a 2v from the whole equation.

Answer 4

u^4 -3u^2 -4
(u^2-4)(u^2+1)
(u-1)(u+1)(u^2 +1)

2u^2v-18uv+28v
2v(u^2 -9u + 14)
2v(u-7)(u-2)

Answer 5

(u^2-4)(u^2+1)
u^2=4
u=2 or u=-2
u^2=-1
u=i or u=-i