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 x2 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 - x2 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 x2 + 4 - 6 y2 + 7
2 x y and - 3 y x are the only like terms
c) In the expression 9 x2 y + 6 y x + 5 x2 y + 4 + 4 y2
9 x2 y and 5 x2 y are the only like terms
Answer the Following Questions
-
List all terms in and give the coefficient and degree for each in the algebraic expression below.
- 2x + 2
- x + 5y - 9
- - x - y - 7
-
2 x2 - 9
-
- x y2 - 9 x + 6
- x2 y2 - 6 x3 + 8
- 2x + 2
-
Equivalent expressions have the same terms. Which of the following expressions are equivalent?
- 2x + 2 y - 3
-
2 x2 - 9
-
2 y2 + 2 x - 3
-
- 9 + 2 x2
- 2 y - 3 + 2x
-
3 + 2 y2 + 8 x
-
8x - 3 - 2 y2
-
- 3 - 2 y2 + 8 x
- - 3 + 2 y + 2 x
- 2x + 2 y - 3
-
List all like terms in each of the following expressions?
- 2 x - 2 y + 10
- 8 x - 5 y + 7 - 2 x
- 2 x + 2 y + 7 + 3 x + 6 y - 8
- x + 7 - x + 4
-
2 x2 + 5 - x2 - 3
-
2 y2 x - y x + 6 + 5 x y2 + 3 x y - 3
- 2 x - 2 y + 10
Solutions to the Above Questions
-
Solution
Terms are separated by operators. The coefficient and degree of a term has been defined above.
expression terms in the expression terms with
coefficients and
exponents highlightedcoefficient of each term
(red)degree of
each term
( blue)2 x + 2 2 x
+ 2(2) x 1
+ 22
constant term1
0x + 5 y - 9 x
+ 5 y
- 9(1) x 1
(+5) y 1
- 91
+ 5
constant term1
1
0- x - y - 7 - x
- y
- 7(-1) x 1
(-1) y 1
- 7- 1
- 1
constant term1
1
02 x2 - 9 2 x2
- 9(2) x 2
- 92
constant term2
0- x y2 - 9 x + 6 - x y2
- 9 x
+ 6(- 1) x 1 y 2
(- 9) x 1
+ 6-1
-9
constant term1 + 2 = 3
1
0x2 y2 - 6 x3 + 8 x2 y2
- 6 x3
+ 8(1) x 2 y 2
(- 6) x 3
+ 81
- 6
constant term2+ 2 = 4
3
0 -
Solution
To compare algebraic expressions, we first order them from the term with the highest degree to the lowest.
expression ordered a) 2 x + 2 y - 3 = 2 x + 2 y - 3 b) 2 x2 - 9 = 2 x2 - 9 c) 2 y2 + 2 x - 3 = 2 y2 + 2 x - 3 d) - 9 + 2 x2 = 2 x2 - 9 e) 2 y - 3 + 2 x = 2 x + 2 y - 3 f) 3 + 2 y2 + 8 x = 2 y2 + 8 x + 3 g) 8 x - 3 - 2 y2 = - 2 y2 + 8 x - 3 h) - 3 - 2 y2 + 8 x = - 2 y2 + 8 x - 3 i) - 3 + 2 y + 2 x = 2x + 2 y - 3 We now use the ordered expressions on the right to compare the given expressions on the left of the table.
Expressions a) , e) and i) are equivalent
Expressions b) and d) are equivalent
Expressions g) and h) are equivalent
Expressions c) and f) have no equivalent
-
Solution
Like terms have same variable with the same exponents. Numbers are like terms.
expression like terms in groups a) 2 x - 2 y + 10 no like terms in this expression b) 8 x - 5 y + 7 - 2 x 8 x , - 2 x are like terms c) 2 x + 2 y + 7 + 3 x + 6 y - 8 2x and 3x are like terms
2 y and 6 y are like terms
7 and - 8 are like termsd) x + 7 - x + 4 x and - x are like terms e) 2 x2 + 5 - x2 - 3 2 x2 and - x2 are like terms
+ 5 and - 3 are like termsf) 2 y2 x - y x + 6 + 5 x y2 + 3 x y - 3 2 y2 x and + 5 x y2
- x y and + 3 x y are like terms
6 and - 3 are like terms
References and Links
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