The expression given is \( A = (x + 7)(x - 4)(x + 1)(x + 5) \). To expand this expression, we can multiply the factors step by step.

### Step 1: Multiply the first two factors
\[
(x + 7)(x - 4) = x(x - 4) + 7(x - 4) = x^2 - 4x + 7x - 28 = x^2 + 3x - 28
\]

### Step 2: Multiply the last two factors
\[
(x + 1)(x + 5) = x(x + 5) + 1(x + 5) = x^2 + 5x + x + 5 = x^2 + 6x + 5
\]

### Step 3: Multiply the results from Step 1 and Step 2
\[
(x^2 + 3x - 28)(x^2 + 6x + 5)
\]
We'll expand this by multiplying each term in the first polynomial by each term in the second polynomial.

\[
= x^2(x^2 + 6x + 5) + 3x(x^2 + 6x + 5) - 28(x^2 + 6x + 5)
\]

Expanding this:

\[
= x^4 + 6x^3 + 5x^2 + 3x^3 + 18x^2 + 15x - 28x^2 - 168x - 140
\]

Now, combine like terms:

\[
= x^4 + 9x^3 - 5x^2 - 153x - 140
\]

So, the expanded form of \( A \) is:

\[
A = x^4 + 9x^3 - 5x^2 - 153x - 140
\]

Would you like any more details or explanations on how this expansion was done?

### Related Questions:
1. How do you factor a polynomial like the one we just expanded?
2. What is the significance of the degree of a polynomial?
3. How can you determine the roots of a polynomial?
4. How would you approach multiplying three or more binomials?
5. What is the role of the distributive property in polynomial multiplication?

### Tip:
When expanding multiple binomials, it’s often helpful to first group and expand pairs of binomials before combining them into a final product.

Learn how to expand the polynomial (x+7)(x-4)(x+1)(x+5) step-by-step with a detailed solution. This problem covers key algebraic concepts such as polynomial multiplication and expansion. Suitable for advanced high school students (Grades 10-12).

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