Certainly! Let’s walk through the steps used by Lorne to subtract [tex]\(6x^3 - 2x + 3\)[/tex] from [tex]\(-3x^3 + 5x^2 + 4x - 7\)[/tex].
1. Step 1: Set up the subtraction problem as addition by adding the negative of the second polynomial.
[tex]\[
\left(-3x^3 + 5x^2 + 4x - 7\right) + \left(-6x^3 + 2x - 3\right)
\][/tex]
2. Step 2: Clearly distribute and separate each term from the two polynomials.
[tex]\[
\left(-3x^3\right) + 5x^2 + 4x + (-7) + \left(-6x^3\right) + 2x + (-3)
\][/tex]
3. Step 3: Group like terms together.
[tex]\[
\left[\left(-3x^3\right) + \left(-6x^3\right)\right] + [4x + 2x] + [(-7) + (-3)] + \left[5x^2\right]
\][/tex]
4. Step 4: Simplify each group of like terms.
[tex]\[
-9x^3 + 6x + (-10) + 5x^2
\][/tex]
5. Step 5: Rewrite the final simplified polynomial.
[tex]\[
-9x^3 + 5x^2 + 6x - 10
\][/tex]
This step-by-step solution clearly illustrates how Lorne subtracted the polynomials and combined like terms to arrive at the final expression.
