Question

Prove that these 3 equations are the same. There is more than one way to do this. Show in multipleways for a higher score.y = (x + 5)(x + 1)y = (x + 3)^2 - 4y = x^2 + 6x + 5

Answer 1

For the first equation:

y = (x + 5)(x + 1)

apply distribution property:

y = (x + 5)(x) + (x + 5)(1)

y = x·x + 5·x + x·1 + 5·1

y = x² + 5x + x + 5

y = x² + 6x + 5

For the second equation:

y = (x + 3)² - 4

use the fact that (a + b)² = a² + 2ab + b², for the term (x + 3)², then, you have:

y = x² + 2·x·3 + 3² - 4

y = x² + 6x + 9 - 4

y = x² + 6x + 5

The third equation is already in the convenient form.

Then, you can notice that all three equations are the same equations.