b) \( \left(x^{3}+3 x^{2}+1\right)\left(3 x^{2}+6 x-2\right) \)

We want to multiply the two polynomials:   (x³ + 3x² + 1)(3x² + 6x − 2). Step 1. Distribute each term in the first polynomial by multiplying it with every term in the second polynomial. Multiply x³ by each term:   • x³ · 3x² = 3x⁵   • x³ · 6x = 6x⁴   • x³ · (−2) = −2x³ Multiply 3x² by each term:   • 3x² · 3x² = 9x⁴   • 3x² · 6x = 18x³   • 3x² · (−2) = −6x² Multiply 1 by each term:   • 1 · 3x² = 3x²   • 1 · 6x = 6x   • 1 · (−2) = −2 Step 2. Write all the products together:   3x⁵ + 6x⁴ − 2x³ + 9x⁴ + 18x³ − 6x² + 3x² + 6x − 2 Step 3. Combine like terms:   • x⁵-term:  3x⁵   • x⁴-terms: 6x⁴ + 9x⁴ = 15x⁴   • x³-terms: −2x³ + 18x³ = 16x³   • x²-terms: −6x² + 3x² = −3x²   • x-term:  6x   • Constant: −2 The final result becomes:   3x⁵ + 15x⁴ + 16x³ − 3x² + 6x − 2 That is the expanded form of (x³ + 3x² + 1)(3x² + 6x − 2).