Expand: `(5x-3y+2) (5x + 3y + 2)`

Answer

To expand the expression \((5x - 3y + 2)(5x + 3y + 2)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s how to do it step by step:

### Step 1: Distribute each term in the first bracket to each term in the second bracket.

We will multiply each term in the first bracket by each term in the second bracket:

\[ (5x - 3y + 2)(5x + 3y + 2) = 5x(5x + 3y + 2) - 3y(5x + 3y + 2) + 2(5x + 3y + 2) \]

### Step 2: Multiply \(5x\) by each term in the second bracket.

\[ 5x(5x) + 5x(3y) + 5x(2) = 25x^2 + 15xy + 10x \]

### Step 3: Multiply \(-3y\) by each term in the second bracket.

\[ -3y(5x) - 3y(3y) - 3y(2) = -15xy - 9y^2 - 6y \]

### Step 4: Multiply \(2\) by each term in the second bracket.

\[ 2(5x) + 2(3y) + 2(2) = 10x + 6y + 4 \]

### Step 5: Combine all the results from the multiplications.

Now we combine all the terms we calculated:

\[ 25x^2 + 15xy + 10x - 15xy - 9y^2 - 6y + 10x + 6y + 4 \]

### Step 6: Combine like terms.

- The \(xy\) terms: \(15xy - 15xy = 0\)
- The \(x\) terms: \(10x + 10x = 20x\)
- The \(y\) terms: \(-6y + 6y = 0\)

Putting it all together, we have:

\[ 25x^2 - 9y^2 + 20x + 4 \]

### Final Result:
The expanded form of \((5x - 3y + 2)(5x + 3y + 2)\) is:

\[ 25x^2 - 9y^2 + 20x + 4 \]

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