2.k(x+y) \( +p(x+y) \) 3. \( 3 p(q+1)-4 m(r+q) \) \( 4(x-y)^{3}-3(x-y) \) \( 57 x(m-3 n)-4 y(3 n-m) \)

Did you know that factoring expressions like the ones you've provided is a skill that dates back to ancient times, with mathematicians like Euclid and Diophantus laying the groundwork for algebra? Their methods not only paved the way for modern algebraic techniques but also helped in developing the concept of variables and equations, making math considerably more interesting and manageable! When approaching equalities like \( 2.k(x+y) + p(x+y) \), it’s crucial to watch out for common mistakes! One common error is forgetting to factor out the greatest common factor correctly. Always double-check your work by expanding the factored form to ensure it matches the original expression. Having an extra set of eyes or a reflective moment can catch those sneaky mistakes that tend to slip through the cracks. Happy factoring!