Question

describing steps to find the difference

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)

combined like terms
grouped like terms
wrote as addition of the additive inverse
wrote terms as addition of opposite

Explanation:

Analyze the subtraction setup and Step 1

Lorne subtracted \(6x^3 - 2x + 3\) from \(-3x^3 + 5x^2 + 4x - 7\).
The subtraction is written as:

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

In Step 1, Lorne writes:

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

This step changes subtraction to addition of the opposite (or addition of the additive inverse).
Thus, Step 1 is: "wrote as addition of the additive inverse" (or "wrote terms as addition of opposite").

Analyze Step 2 and Step 3

In Step 2, Lorne writes:

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

This rewrites subtraction of terms as addition of their opposites.
In Step 3, Lorne writes:

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

This groups the like terms together.
Thus, Step 3 is: "grouped like terms".

Analyze Step 4 and Step 5

In Step 4, Lorne simplifies the grouped terms:

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

This combines the like terms.
Thus, Step 4 is: "combined like terms".
In Step 5, Lorne rearranges the terms into standard form:

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

Answer:

Based on the mathematical steps shown in the image, the descriptions for each step are:

• Step 1: wrote as addition of the additive inverse
• Step 2: wrote terms as addition of opposite
• Step 3: grouped like terms
• Step 4: combined like terms