Multiply. \[ \left(7 x^{3}+2\right)\left(3 x^{2}+6 x+5\right) \] \( \left(7 x^{3}+2\right)\left(3 x^{2}+6 x+5\right)=\square \) (Simplify your answer.)

To multiply the polynomials \((7x^3 + 2)(3x^2 + 6x + 5)\), we will use the distributive property, also known as the FOIL method for binomials, although here we have a trinomial. 1. Distribute \(7x^3\) to each term in the second polynomial: \[ 7x^3 \cdot 3x^2 = 21x^5 \] \[ 7x^3 \cdot 6x = 42x^4 \] \[ 7x^3 \cdot 5 = 35x^3 \] 2. Now distribute \(2\) to each term in the second polynomial: \[ 2 \cdot 3x^2 = 6x^2 \] \[ 2 \cdot 6x = 12x \] \[ 2 \cdot 5 = 10 \] 3. Now combine all these terms: \[ 21x^5 + 42x^4 + 35x^3 + 6x^2 + 12x + 10 \] 4. As there are no like terms to combine, the final simplified expression is: \[ \left(7 x^{3}+2\right)\left(3 x^{2}+6 x+5\right) = 21x^5 + 42x^4 + 35x^3 + 6x^2 + 12x + 10 \]