Grade 6 examples and questions on terms in algebraic expressions, with detailed explanations and practice questions.
Definition: An algebraic expression is made up of one or more terms and each term is either a signed number or a signed number multiplied by one or more variables raised to a certain power.
Note: Terms without variables such as \(4\), \(-6\), and \(-7\) are called constant terms.
Definition: The degree of a term is the sum of all powers of the variables in that term.
Definition: The coefficient of a term is the signed number that multiplies the term.
Definition: Like terms are terms with the same variables raised to the same power. Constant terms are like terms.
List all terms and give the coefficient and degree for each in the expressions below.
| Expression | Terms | Coefficient | Degree |
|---|---|---|---|
| \(2x + 2\) | \(2x, 2\) | \(2, \text{const}\) | \(1, 0\) |
| \(x + 5y - 9\) | \(x, 5y, -9\) | \(1, 5, \text{const}\) | \(1, 1, 0\) |
| \(-x - y - 7\) | \(-x, -y, -7\) | \(-1, -1, \text{const}\) | \(1, 1, 0\) |
| \(2x^2 - 9\) | \(2x^2, -9\) | \(2, \text{const}\) | \(2, 0\) |
| \(-xy^2 - 9x + 6\) | \(-xy^2, -9x, 6\) | \(-1, -9, \text{const}\) | \(3, 1, 0\) |
| \(x^2y^2 - 6x^3 + 8\) | \(x^2y^2, -6x^3, 8\) | \(1, -6, \text{const}\) | \(4, 3, 0\) |
Equivalent expressions have the same terms. Which of the following expressions are equivalent?
By ordering expressions by degree:
| a, e, i | \(2x + 2y - 3\) (Equivalent) |
|---|---|
| b, d | \(2x^2 - 9\) (Equivalent) |
| g, h | \(-2y^2 + 8x - 3\) (Equivalent) |
| c, f | No equivalent pair. |
List all like terms in each of the following expressions:
| Expression | Like Terms |
|---|---|
| \(2x - 2y + 10\) | None |
| \(8x - 5y + 7 - 2x\) | \(8x, -2x\) |
| \(2x + 2y + 7 + 3x + 6y - 8\) | \(2x, 3x\); \(2y, 6y\); \(7, -8\) |
| \(x + 7 - x + 4\) | \(x, -x\); \(7, 4\) |
| \(2x^2 + 5 - x^2 - 3\) | \(2x^2, -x^2\); \(5, -3\) |
| \(2y^2x - yx + 6 + 5xy^2 + 3xy - 3\) | \(2y^2x, 5xy^2\); \(-yx, 3xy\); \(6, -3\) |