(25x-33y)(33y+25x)

To simplify the expression \((25x - 33y)(33y + 25x)\), we can use the distributive property (also known as the FOIL method for binomials). 1. **First**: Multiply the first terms in each binomial: \[ 25x \cdot 25x = 625x^2 \] 2. **Outer**: Multiply the outer terms: \[ 25x \cdot 33y = 825xy \] 3. **Inner**: Multiply the inner terms: \[ -33y \cdot 25x = -825xy \] 4. **Last**: Multiply the last terms: \[ -33y \cdot 33y = -1089y^2 \] Now, combine all these results: \[ 625x^2 + 825xy - 825xy - 1089y^2 \] The \( +825xy \) and \( -825xy \) cancel each other out, so we are left with: \[ 625x^2 - 1089y^2 \] Thus, the simplified expression is: \[ 625x^2 - 1089y^2 \] This expression can also be recognized as a difference of squares, which can be factored further as: \[ (25x)^2 - (33y)^2 = (25x - 33y)(25x + 33y) \] But since the initial expression had specific factors, the final simplified result for \((25x - 33y)(33y + 25x)\) remains: \[ 625x^2 - 1089y^2 \]