Find each of the following products :
`(5x + 7) xx (3x + 4)`

Answer

To find the product of the expressions \( (5x + 7) \) and \( (3x + 4) \), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Distribute \( 5x \)
We start by multiplying \( 5x \) by each term in the second expression \( (3x + 4) \).

\[ 5x \cdot 3x + 5x \cdot 4 \]

Calculating these products:

- \( 5x \cdot 3x = 15x^2 \)
- \( 5x \cdot 4 = 20x \)

So, from this step, we have:

\[ 15x^2 + 20x \]

### Step 2: Distribute \( 7 \)
Next, we multiply \( 7 \) by each term in the second expression \( (3x + 4) \).

\[ 7 \cdot 3x + 7 \cdot 4 \]

Calculating these products:

- \( 7 \cdot 3x = 21x \)
- \( 7 \cdot 4 = 28 \)

So, from this step, we have:

\[ 21x + 28 \]

### Step 3: Combine all the terms
Now, we combine all the terms we obtained from both distributions:

\[ 15x^2 + 20x + 21x + 28 \]

### Step 4: Combine like terms
Next, we combine the like terms \( 20x \) and \( 21x \):

\[ 15x^2 + (20x + 21x) + 28 = 15x^2 + 41x + 28 \]

### Final Answer
Thus, the product of \( (5x + 7) \) and \( (3x + 4) \) is:

\[ \boxed{15x^2 + 41x + 28} \]

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