(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).
First: Multiply the first terms in each binomial: \[ 25x \cdot 25x = 625x^2 \]
Outer: Multiply the outer terms: \[ 25x \cdot 33y = 825xy \]
Inner: Multiply the inner terms: \[ -33y \cdot 25x = -825xy \]
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: \[ 625x^2 - 1089y^2 \]
