Question

1. What is the product?

y3 + 27
y3 – 27
y3 – 6y2 + 27
y3 + 6y2 + 27


2. What is the product of a+3 and −2a2+15a+6b2?

−2a3+9a2+45a+24b2
−2a3+21a2+45a+24b2
−2a3+9a2+45a+6ab2+18b2
−2a3+21a2+45a+6ab2+18b2

3. The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form?

3x3 + 2x2 – x + 3
3x3 + 2x2 – x – 3
3x3 + x2 – 6x + 9
3x3 + x2 + 6x – 9

4. In which step did Fiona make an error?

Step 1
Step 2
Step 3
Step 4

Answer 1

I can solve 2 and 3 with the information given, but I need more context for 1 and 4 (the statement for 1 is ambiguous and 4 refers to "steps" that aren't shown). Please paste the missing steps or clarify question 1. Meanwhile:

2. Multiply (a + 3)(−2a^2 + 15a + 6b^2):
- Expand: a(−2a^2 + 15a + 6b^2) + 3(−2a^2 + 15a + 6b^2)
- = −2a^3 + 15a^2 + 6ab^2 − 6a^2 + 45a + 18b^2
- = −2a^3 + 9a^2 + 45a + 6ab^2 + 18b^2

Answer: −2a^3 + 9a^2 + 45a + 6ab^2 + 18b^2 (the third choice).

3. A = x^2, B = 3x + 2, C = x − 3. Compute AB − C^2:
- AB = x^2(3x + 2) = 3x^3 + 2x^2
- C^2 = (x − 3)^2 = x^2 − 6x + 9
- AB − C^2 = (3x^3 + 2x^2) − (x^2 − 6x + 9) = 3x^3 + x^2 + 6x − 9

Answer: 3x^3 + x^2 + 6x − 9 (the fourth choice).

For 1 and 4: please show the exact product to compute for (1) or the steps Fiona used for (4), and I'll finish those.