Factor completely 3u^4x^4-3x^4

1 answer:

3 0

The greatest common factor in this expression is 3x^4. Let's take it out:

3x^4(u^4 - 1)

u^4 - 1 is a difference of two squares and can be factored further:

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

u^2 - 1 is also a difference of two squares:

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

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Perform the following division:

Radda [10]

Hey!

Alright, the first step to solving this division problem would be to convert the mixed fraction into a simple fraction. To do that, we'll multiply the denominator by the whole number and then add that total to the numerator.

Original Fraction :
$3 \frac{3}{4}$

New Fraction {Changed by Conversion} :
$\frac{15}{4}$

Now that we've successfully done that we'll have to change the equation.

Old Equation :
$\frac{15}{4}$ ÷ $\frac{2}{8}$ = ?

New Equation {Changed by Flipping the Second Fraction and the Symbol} :
$\frac{15}{4}$ · $\frac{8}{2}$ = ?

Now we multiply straight across.

Old Equation :
$\frac{15}{4}$ · $\frac{8}{2}$ = ?

Solved :
$\frac{120}{8}$

Almost done!
Now we have to simplify the fraction.

Old Fraction :
$\frac{120}{8}$

New Fraction {Changed by Simplification} :
$\frac{15}{1}$

Now just convert it to a whole number by removing the fraction line and the number, and that's it!

So, $3 \frac{3}{4}$ ÷ $\frac{2}{8}$ equals 15.

Hope this helps!

- Lindsey Frazier ♥

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Please help and explain how to do this. thank you in advance!

Sholpan [36]

We want to solve
$3e^{2x}+5=27$

Subtract 5 from each side.
$3e^{2x}=22$
Divide each side by 3.
$e^{2x}=7.3333$
Take natural logs of each side.
$2x=ln(7.3333)=1.9924$
Divide each side by 2.
x = 0.9962

Answer: x = 0.996 (nearest thousanth)

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