To multiply a binomial and a trinomial, order the terms by descending exponent, multiply the coefficients and add the exponents of like terms, then combine the terms in descending exponent order. Specifically, (5x^6 + 9x^3 + 3x)(8x^5 + 3x^4) = 40x^11 + 15x^10 + 72x^8 + 27x^7 + 24x^6 + 9x^5.

1. Guide to Multiplying a Binomial and a Trinomial (5x 6 +9x 3 +3x)(8x 5 +3x 4 )

2. Step 1: I put all my numbers in order from the biggest to the smallest exponent. (5x 6 +9x 3 +3x)(8x 5 +3x 4 )

3. Step 2: then I put all of them in the a box and I times the coefficient and added the exponent. 5x 6 9x 3 3x 8x 5 3x 4 9x 5 27x 7 15x 10 24x 6 72x 8 40x 11

4. Step 3: then I put the number by the biggest exponent. 40x 11+ 15x 10 +72x 8 +27x 7 +24x 6 +9x 5

5. Step 4:this is my answer (Show work here) 40x 11 +15x 10 +72x 8 +27x 7 +24x 6 +9x 5