Grade 6 examples and questions on terms in algebraic expressions, with detailed solutions and explanations, are presented.
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.
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
expression | terms in the expression | terms with coefficients and exponents highlighted | coefficient of each term (red) | degree of each term ( blue) |
---|---|---|---|---|
2 x + 2 | 2 x + 2 | (2) x ^{ 1} + 2 | 2 constant term | 1 0 |
x + 5 y - 9 | x + 5 y - 9 | (1) x ^{ 1} (+5) y ^{ 1} - 9 | 1 + 5 constant term | 1 1 0 |
- x - y - 7 | - x - y - 7 | (-1) x ^{ 1} (-1) y ^{ 1} - 7 | - 1 - 1 constant term | 1 1 0 |
2 x^{2} - 9 | 2 x^{2} - 9 | (2) x ^{ 2} - 9 | 2 constant term | 2 0 |
- x y^{2} - 9 x + 6 | - x y^{2} - 9 x + 6 | (- 1) x ^{ 1} y^{ 2} (- 9) x ^{ 1} + 6 |
-1 -9 constant term | 1 + 2 = 3 1 0 |
x^{2} y^{2} - 6 x^{3} + 8 | x^{2} y^{2} - 6 x^{3} + 8 |
(1) x^{ 2} y^{ 2} (- 6) x^{ 3} + 8 |
1 - 6 constant term |
2+ 2 = 4 3 0 |
expression | ordered |
---|---|
a) 2 x + 2 y - 3 | = 2 x + 2 y - 3 |
b) 2 x^{2} - 9 | = 2 x^{2} - 9 |
c) 2 y^{2} + 2 x - 3 | = 2 y^{2} + 2 x - 3 |
d) - 9 + 2 x^{2} | = 2 x^{2} - 9 |
e) 2 y - 3 + 2 x | = 2 x + 2 y - 3 |
f) 3 + 2 y^{2} + 8 x | = 2 y^{2} + 8 x + 3 |
g) 8 x - 3 - 2 y^{2} | = - 2 y^{2} + 8 x - 3 |
h) - 3 - 2 y^{2} + 8 x | = - 2 y^{2} + 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
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 terms |
d) x + 7 - x + 4 | x and - x are like terms |
e) 2 x^{2} + 5 - x^{2} - 3 | 2 x^{2} and - x^{2} are like terms + 5 and - 3 are like terms |
f) 2 y^{2} x - y x + 6 + 5 x y^{2} + 3 x y - 3 | 2 y^{2} x and + 5 x y^{2} - x y and + 3 x y are like terms 6 and - 3 are like terms |