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Algebraic Expressions

A letter can stand for a number. Terms, coefficients, and like terms are the building blocks of algebra.

Letters for Numbers

In algebra, a letter such as x, y, or n stands for a number. It might be a number you do not know yet, or a number that can change. An algebraic expression is a group of numbers and letters joined by + , - , \times , or \div, but with no equals sign. " 3 x + 2 " is an expression. " 3 x + 2 = 11 " is an equation — that comes later.

Multiplication signs are usually left out in algebra. 5 \times x is written 5 x . x \times y is written xy. This is shorter, and it is the standard way algebra is written everywhere.

Example 1 — naming the parts

Look at the expression 4 x + 7 . 1 There are two terms: 4 x and 7 . 2 4 x has coefficient 4 and letter x . 3 7 is a term on its own, called a constant term (it never changes).

Example 2 — a longer expression

Look at the expression 3 x^{2} - 2 x + 5 . 1 There are three terms: 3 x^{2}, - 2 x, and 5 . 2 3 x^{2} means 3 \times x \times x . The coefficient is 3 . 3 - 2 x has coefficient - 2 . 4 5 is the constant term.

Example 1 — spotting like terms

In 5 x + 3 y - 2 x + y, which terms are like terms? 1 5 x and - 2 x both have just x . They are like terms. 2 3 y and y both have just y . They are like terms. 3 There is no term with both x and y, so x -terms and y -terms never combine with each other.

Practice

In the expression 7 a - 3 b + 2 a, which terms are like terms?

Letters for Numbers

In algebra, a letter such as x, y, or n stands for a number. It might be a number you do not know yet, or a number that can change. An algebraic expression is a group of numbers and letters joined by + , - , \times , or \div, but with no equals sign. " 3 x + 2 " is an expression. " 3 x + 2 = 11 " is an equation — that comes later.

Multiplication signs are usually left out in algebra. 5 \times x is written 5 x . x \times y is written xy. This is shorter, and it is the standard way algebra is written everywhere.

Example 1 — naming the parts

Look at the expression 4 x + 7 . 1 There are two terms: 4 x and 7 . 2 4 x has coefficient 4 and letter x . 3 7 is a term on its own, called a constant term (it never changes).

Example 2 — a longer expression

Look at the expression 3 x^{2} - 2 x + 5 . 1 There are three terms: 3 x^{2}, - 2 x, and 5 . 2 3 x^{2} means 3 \times x \times x . The coefficient is 3 . 3 - 2 x has coefficient - 2 . 4 5 is the constant term.

Like Terms

Example 1 — spotting like terms

In 5 x + 3 y - 2 x + y, which terms are like terms? 1 5 x and - 2 x both have just x . They are like terms. 2 3 y and y both have just y . They are like terms. 3 There is no term with both x and y, so x -terms and y -terms never combine with each other.

Practice

In the expression 7 a - 3 b + 2 a, which terms are like terms?