Grade 6 examples and questions on adding and subtracting like terms with detailed solutions and explanations are presented. The solutions are at the bottom of this page.
Review
In an algebraic expression, like terms are all terms with the same variable having the same powers.
Examples
1) 2 x , 4x , x and 10 x are all like terms with coefficients 2, 4, 1 and 10 respectively.(Note that the coefficient of like terms may be different).
2) In the algebraic expression: 2x + 7x  6 + 4 x^{2}  6x , the terms 2 x, 7 x and  6 x are all like terms: they have the same variable x to the same power 1.
Like terms are important because they can be added and subtracted and hence lead to the simplifications of algebraic expressions.
How to add and subtract like terms in an algebraic expression?
We add and/or subtract like terms by adding their coefficients.
Examples
3) Simplify, by adding and subtracting, the expression: 3 x + 10 + 5 x  6 x  4
3 x + 10 + 5 x  6 x  4 given
= (3 x + 5 x  6 x) + (10  4) use parentheses to put like terms together
= (3 + 5  6) x + (10  4) identify coefficients and put variable out of parentheses (factoring)
= 2 x + 6 add and/or subtract coefficients and numbers to simplify
4) Use distributive property , then add and subtract to simplify the expression 2(x  3) + 3(x + 1)
Use distributive property: 2(x  3) = (2)(x) + (2)(3) = 2 x  6 and 3(x + 1) = (3)(x) + (3)(1) = 3 x + 3
We now write the whole expression: 2(x  3) + 3(x + 1) = 2 x  6 + 3 x + 3
Group like terms : = (2 x + 3 x) + (  6 + 3 ) = ( 2 + 3) x + (  6 + 3 ) = 5 x  3
Note that all real numbers are like terms because they can be added and subtracted.
