Find each of the following products :
`(7x + 2y) xx (x + 4y)`

Answer

To find the product of the expressions \( (7x + 2y) \) and \( (x + 4y) \), we can use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Distribute \( 7x \) to both terms in the second expression \( (x + 4y) \)
\[ 7x \cdot x + 7x \cdot 4y \]
Calculating these gives:
\[ 7x^2 + 28xy \]

### Step 2: Distribute \( 2y \) to both terms in the second expression \( (x + 4y) \)
\[ 2y \cdot x + 2y \cdot 4y \]
Calculating these gives:
\[ 2xy + 8y^2 \]

### Step 3: Combine all the terms obtained from the distributions
Now we combine the results from Step 1 and Step 2:
\[ 7x^2 + 28xy + 2xy + 8y^2 \]

### Step 4: Combine like terms
The like terms here are \( 28xy \) and \( 2xy \):
\[ 7x^2 + (28xy + 2xy) + 8y^2 = 7x^2 + 30xy + 8y^2 \]

### Final Answer
Thus, the product of \( (7x + 2y)(x + 4y) \) is:
\[ \boxed{7x^2 + 30xy + 8y^2} \]

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