Question

(u+1)² • (10u-10)² ———————— = 100-100u³ • 1-u²

Answer 1

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Answer 2

Let's simplify the given expression step by step:

First, let's expand the squares:

(u + 1)² = (u + 1)(u + 1) = u² + 2u + 1 (10u - 10)² = (10u - 10)(10u - 10) = 100u² - 200u + 100

Next, substitute these values into the expression:

(u² + 2u + 1)(100u² - 200u + 100) ———————— = 100 - 100u³ • (1 - u²)

Now, let's perform the multiplication in the numerator:

(u² + 2u + 1)(100u² - 200u + 100) = 100u^4 - 200u^3 + 100u^2 + 200u^3 - 400u^2 + 200u + 100u^2 - 200u + 100

Simplify further:

= 100u^4 - 400u^2 + 100

Now, the expression becomes:

(100u^4 - 400u^2 + 100) ———————— = 100 - 100u³ • (1 - u²)

Now, let's factor out the common terms from the numerator:

100(u^4 - 4u^2 + 1) = 100(u^2 - 1)^2

The expression is now:

100(u^2 - 1)^2 ———————— = 100 - 100u³ • (1 - u²)

Now, we can cancel out the common term "100" from both sides of the equation:

(u^2 - 1)^2 = 1 - u³ • (1 - u²)

Finally, let's expand the square on the left-hand side:

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

So, the simplified equation is:

u^4 - 2u^2 + 1 = 1 - u³ • (1 - u²)

Now, let's move all terms to one side to set the equation to zero:

u^4 - 2u^2 + u³ • (1 - u²) = 0

This is the simplified expression for the given equation.