Basic Operations

Combining Like Terms

The process of simplifying an expression by adding together or subtracting terms that have the same variable factors is called combining like terms.

Example:

Simplify the expression 2x − 5y − x + 7y.

2x − 5y − x + 7y = (2x − x) + (7y − 5y) = x + 2y

Notice that the commutative, associative, and distributive laws that govern arithmetic operations with ordinary numbers also apply to algebraic terms and polynomials.

Adding and Subtracting Polynomials

To add or subtract polynomials, combine like terms.

(3x² + 5x + 7) − (x² + 12) = (3x² − x²) + 5x + (7 − 12) = 2x² + 5x − 5

Factoring Algebraic Expressions

Factoring a polynomial means expressing it as a product of two or more simpler expressions. Common factors can be factored out by using the distributive law.

Example:

Factor the expression 2a + 6ac.

The greatest common factor of 2a + 6ac is 2a. Using the distributive law, you can factor out 2a so that the expression becomes 2a(1 + 3c).

Example:

All three terms in the polynomial 3x³ + 12x² − 6x contain a factor of 3x. Pulling out the common factor yields 3x(x² + 4x − 2).