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We are asked to expand the expression \((x - 5)(x^2 + 7x + 6)\) into a polynomial in standard form.

To do this, we apply the distributive property (also known as the FOIL method for binomials). We multiply each term in \((x - 5)\) by each term in \((x^2 + 7x + 6)\):

### Step-by-step expansion:
1. Multiply \(x\) by each term in \((x^2 + 7x + 6)\):
   - \(x \cdot x^2 = x^3\)
   - \(x \cdot 7x = 7x^2\)
   - \(x \cdot 6 = 6x\)

2. Multiply \(-5\) by each term in \((x^2 + 7x + 6)\):
   - \(-5 \cdot x^2 = -5x^2\)
   - \(-5 \cdot 7x = -35x\)
   - \(-5 \cdot 6 = -30\)

### Combine like terms:
Now, we add the results from each multiplication:
\[
x^3 + 7x^2 + 6x - 5x^2 - 35x - 30
\]

Group the like terms:
\[
x^3 + (7x^2 - 5x^2) + (6x - 35x) - 30
\]

Simplify:
\[
x^3 + 2x^2 - 29x - 30
\]

Thus, the expanded polynomial in standard form is:
\[
x^3 + 2x^2 - 29x - 30
\]

Would you like further details or have any questions about this process?

Here are 5 related questions for you:
1. How do you factor a cubic polynomial like \(x^3 + 2x^2 - 29x - 30\)?
2. Can this expanded polynomial be factored further into simpler terms?
3. How does the FOIL method differ when applied to binomials versus polynomials?
4. What is the degree of the polynomial \(x^3 + 2x^2 - 29x - 30\)?
5. How would the polynomial change if the original expression was \((x + 5)(x^2 + 7x + 6)\)?

**Tip:** When expanding polynomials, organizing your work and multiplying terms step by step helps avoid mistakes and makes it easier to combine like terms.

Expand the expression to a polynomial in standard form: (x - 5)(x^2 + 7x + 6)

Learn how to expand the polynomial expression (x - 5)(x^2 + 7x + 6) into its standard form. This problem covers the distributive property and step-by-step expansion of polynomials, suitable for students in Grades 9-11.

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