Expand (x+m)(3/4+5x): Step-by-Step Binomial Multiplication

To solve this problem, we'll follow these steps:

• Step 1: Apply the distributive property to expand the expression.

• Step 2: Perform the multiplication for each pair of terms.

• Step 3: Combine any like terms.

Now, let's work through each step:
Step 1: We have the expression $(x + m)(\frac{3}{4} + 5x)$. We'll distribute each term in the first binomial across each term in the second binomial.
Step 2: The expression expands by distributing as follows: $x(\frac{3}{4}) + x(5x) + m(\frac{3}{4}) + m(5x)$.
Step 3: Perform the multiplications: $\frac{3}{4}x + 5x^2 + \frac{3}{4}m + 5mx$.

Note that there are no like terms to combine further.

Therefore, the solution to the problem is $\frac{3}{4}x + 5x^2 + \frac{3}{4}m + 5mx$.