To multiply and simplify the expressions (x²+3x+1)(x²+4x+2), you can use the distributive property. Here's how you can do it step by step:
1. Multiply each term in the first expression by each term in the second expression:
(x²)(x²) + (x²)(4x) + (x²)(2) + (3x)(x²) + (3x)(4x) + (3x)(2) + (1)(x²) + (1)(4x) + (1)(2)
2. Simplify each multiplication:
x^4 + 4x³ + 2x² + 3x³ + 12x² + 6x + x² + 4x + 2
3. Combine like terms:
x^4 + 7x³ + 13x² + 10x + 2
Therefore, the product of (x²+3x+1)(x²+4x+2) simplifies to x^4 + 7x³ + 13x² + 10x + 2.
