Operations on Polynomials: Identifying Like Terms, Algebraic Addition, and Subtraction Rules

In this lesson, we establish the fundamental operational rules for adding and subtracting algebraic expressions. The cornerstone requirement for combining terms is the concept of 'Like Terms'. Two or more algebraic terms are strictly classified as 'like' if and only if they possess identical variable letters raised to identical corresponding powers, regardless of whether their numerical coefficients differ: for example, 5x²y and -3x²y are like terms, whereas 5x²y and 5xy² are unlike terms because the exponents do not match. When adding like terms, we add only their numerical coefficients while keeping the variable factors unchanged: (ax + bx = (a + b)x). Unlike terms can never be merged. For subtracting expressions, the phrased problem 'Subtract A from B' mathematically signifies calculating (B - A). The golden rule of algebraic subtraction is to reverse the signs of every single term in the subtrahend (A) and then proceed with algebraic addition.