To simplify the expression $(4x + 7)(x^2 + x - 6)$, we will expand the terms using the distributive property (also known as FOIL for binomials). Here's the step-by-step breakdown:

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

We will multiply each term in $(4x + 7)$ by each term in $(x^2 + x - 6)$:

1. $4x \times x^2 = 4x^3$
2. $4x \times x = 4x^2$
3. $4x \times -6 = -24x$
4. $7 \times x^2 = 7x^2$
5. $7 \times x = 7x$
6. $7 \times -6 = -42$

Now, add all the terms together:

$4x^3 + 4x^2 - 24x + 7x^2 + 7x - 42$

Next, combine like terms:

• $4x^2 + 7x^2 = 11x^2$
• $-24x + 7x = -17x$

Thus, the simplified expression is:

$4x^3 + 11x^2 - 17x - 42$

Would you like any further explanation?

Related Questions:

1. How do you factor cubic polynomials?
2. What is the distributive property in algebra?
3. Can this expression be factored further?
4. How do you solve for roots in a cubic equation?
5. What are the applications of polynomial expansion?

Tip:

When expanding polynomials, always keep track of like terms to simplify the final expression easily.