Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the dif

To simplify the expression:
-(6 x^3 - 2 x + 3) - 3 x^3 + 5 x^2 + 4 x - 7

Start with - (6 x^3 - 2 x + 3) = -6 x^3 + 2 x - 3:
-6 x^3 + 2 x - 3 - 3 x^3 + 5 x^2 + 4 x - 7

Next, combine similar terms: -3 x^3 - 6 x^3 + 5 x^2 + 4 x + 2 x - 7 - 3 = (-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3):
(-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3)

-3 x^3 - 6 x^3 results in -9 x^3:
-9 x^3 + 5 x^2 + (4 x + 2 x) + (-7 - 3)

Combine 4 x and 2 x to get 6 x:
-9 x^3 + 5 x^2 + 6 x + (-7 - 3)

The operation -7 - 3 yields -10:
-9 x^3 + 5 x^2 + 6 x - 10

Factoring out -1 from -9 x^3 + 5 x^2 + 6 x - 10 leads to:
Final Answer: - (9 x^3 - 5 x^2 - 6 x + 10)

Step-by-step Breakdown:

We begin by subtracting

1.  

2.  Applying the negative sign in the second bracket and listing all terms separately

3. Merging terms that are alike

4. Summing the terms with identical x powers

5. Organizing the terms from highest to lowest powers of x