Question

lorne subtracted (6x^3 - 2x + 3) from (-3x^3 + 5x^2 + 4x - 7). use the drop - down menus to identify the steps lorne used to find the difference.

1. ((-3x^3 + 5x^2 + 4x - 7)+(-6x^3 + 2x - 3))
2. ((-3x^3)+5x^2 + 4x+(-7)+(-6x^3)+2x+(-3))
3. ((-3x^3)+(-6x^3)+4x + 2x+(-7)+(-3)+(5x^2))
4. (-9x^3 + 6x+(-10)+5x^2)
5. (-9x^3 + 5x^2 + 6x - 10)

Explanation:

Step1: Rewrite subtraction as addition

$(-3x^3 + 5x^2 + 4x - 7) + (-6x^3 + 2x - 3)$

Step2: Rewrite terms with sign

$(-3x^3) + 5x^2 + 4x + (-7) + (-6x^3) + 2x + (-3)$

Step3: Group like terms

$[(-3x^3) + (-6x^3)] + [4x + 2x] + [(-7) + (-3)] + 5x^2$

Step4: Combine like terms

$-9x^3 + 6x + (-10) + 5x^2$

Step5: Rearrange into standard form

$-9x^3 + 5x^2 + 6x - 10$

Answer:

The completed steps (matching each line) are:

1. Rewrite subtraction as addition
2. Rewrite terms with their signs
3. Group like terms together
4. Combine like terms
5. Rearrange into standard polynomial form

Final simplified difference: $\boldsymbol{-9x^3 + 5x^2 + 6x - 10}$