Find each of the following products :
`(9x + 5y) xx (4x + 3y)`

Answer

To find the product of the algebraic expressions \( (9x + 5y) \) and \( (4x + 3y) \), we will use the distributive property (also known as the FOIL method for binomials). Here are the steps to solve the problem:

### Step 1: Distribute \( 9x \) to both terms in the second expression.
\[ 9x \cdot (4x + 3y) = 9x \cdot 4x + 9x \cdot 3y \]
Calculating these:
\[ 9x \cdot 4x = 36x^2 \]
\[ 9x \cdot 3y = 27xy \]

### Step 2: Distribute \( 5y \) to both terms in the second expression.
\[ 5y \cdot (4x + 3y) = 5y \cdot 4x + 5y \cdot 3y \]
Calculating these:
\[ 5y \cdot 4x = 20xy \]
\[ 5y \cdot 3y = 15y^2 \]

### Step 3: Combine all the terms obtained from the distributions.
Now we combine the results from Step 1 and Step 2:
\[ 36x^2 + 27xy + 20xy + 15y^2 \]

### Step 4: Combine like terms.
The like terms here are \( 27xy \) and \( 20xy \):
\[ 27xy + 20xy = 47xy \]

### Final Expression:
Putting it all together, we have:
\[ 36x^2 + 47xy + 15y^2 \]

Thus, the product of \( (9x + 5y) \) and \( (4x + 3y) \) is:
\[ \boxed{36x^2 + 47xy + 15y^2} \]

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