What is the second quadratic expression if the sum of two quadratic expressions is three times their difference and the first expression is 4x^2 - 6x + 10?

To determine why the second quadratic expression, which you're considering to be 2x² - 3x + 5, meets the given condition where the sum of two quadratic expressions is three times their difference, let’s first write down both expressions. The first expression is 4x² - 6x + 10, and the second expression is 2x² - 3x + 5.

Let's denote the first expression as ( Q_1 = 4x^2 - 6x + 10 ) and the second expression as ( Q_2 = 2x^2 - 3x + 5 ).

Now, calculate the sum of ( Q_1 ) and ( Q_2 ):

[

Q_1 + Q_2 = (4x^2 - 6x + 10) + (2x^2 - 3x + 5) = 6x^2 - 9x + 15

]

Next, calculate the difference of ( Q_1 ) and ( Q_2 ):

[

Q_1 - Q_2 = (4x^2 - 6x + 10) - (2x