# Terms in Algebraic Expressions - Grade 6

Grade 6 examples and questions on terms in algebraic expressions, with detailed solutions and explanations, are presented.

__Algebraic Expression__

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.

__Example 1__

2x + 4 is called an algebraic expression

it has two terms 2 x and 4

__Example 2__

-3 x^{2} - x - 6 is another expression and it has 3 terms: -3 x^{2} , - x and - 6

__Example 3__

- 5 x y - (3 / 4) x + y - 7 is another expression and it has 4 terms: - 5 x y, - (3 / 4) x , y and - 7

Note

Terms without variable such as 4, - 6 and -7 are called constant terms.

__Degree of a Term__

Definition: The degree of a term is the sum of all powers of the variables in that term

a) The degree of the term 2 x is 1 because 2 x means 2 x^{ 1} and 1 is the power of x.

b) The degree of the term -3 x^{2} is 2 because 2 is the power of x

c) The degree of the term - 5 x y in example 3 is 2 because the power of x is 1 and the power of y is 1 and degree of the term is the sum of the two powers.

d) The degree of the term - x^{2} y is 3 because the power of x is 2 and the power of y is 1 and degree of the term is the sum of the two powers.

e) The degree of a constant term such as 4, - 6 and - 7 is zero.

__Coefficient of a Term__

Definition: The coefficient of a term is the signed number that multiplies the term

a) The coefficient of the term 2 x which can be written as (2) x is 2

b) The coefficient of the term - 3 x^{2} which can be written as (-3) x^{2} is - 3

c) The coefficient of the term - x which can be written as (-1) x is - 1

d) The coefficeient of the term y which can be written as (1) y is 1

__Like Terms__

Definition: Like terms are terms with the same variables raised to the same power. Constant terms are like terms

a) In the expression 2 x + 3 y - 5 x + 4 - 6 y + 7

2 x and - 5x are like terms : same variable x to the same power 1

3 y and - 6 y are like terms: same variable y to the same power 1

4 and 7 are constants and therefore like terms

b) In the expression 2 x y - 3y x - 5 x^{2} + 4 - 6 y^{2} + 7

2 x y and - 3 y x are the only like terms

c) In the expression 9 x^{2} y + 6 y x + 5 x^{2} y + 4 + 4 y^{2}

9 x^{2} y and 5 x^{2} y are the only like terms

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