to view answer.
The terms in an expression are the pieces of the expression that are being added together. Terms can be numbers, variables, or variables with coefficients.
For example, consider the following expression:
$$3x+2y-7x^2 +4-y+4y+x^2 +x$$
This expression can be rewritten as $$3x+2y+(-7x^2)+4+(-y)+4y+x^2+x$$
Thus, $$3x, \; 2y,\; -7x^2, \;4, \; -y,\; 4y,\; x^2,\; x$$
Note that since positive $$y$$ was subtracted within the expression, this is the same as adding the term $$-y$$. It is best to consider adding all terms. Turning subtraction into the addition of negative numbers is often helpful in keeping the correct signs.
Like terms refer to the terms that contain the same variable as well as the same exponent on the variable. These like terms can be combined, or added together. For instance, in this expression, the “x” terms, $$x$$ and $$3x$$ can be combined to get a total of $$4x$$. However, $$x^2$$ and $$4x$$ are not like terms; one of the “x” variables has an exponent of 1 and the other has an exponent of 2. Thus, we cannot combine $$4x$$ and $$x^2$$.
The like terms in this example are highlighted:
$$\color{red}{3x}\color{black}{+}\color{blue}{2y}\color{black}{-}\color{green}{7x^2}\color{black} {+}\color{orange}{4} \color{black}{}\color{blue}{y}\color{black}{+}\color{blue}{4y}\color{black}{+}\color{green}{x^2}\color{black}{+}\color{red}{x}$$
So, we can combine all like terms in the expression:
$$\eqalign{&{\color{red}{(3x+x)} } &{\color{black}{+}} {\color{blue}{(2y-y+4y)}} &{\color{black}{+}} {\color{green}{(-7x^2+x^2)}} &{\color{black}{+}} {\color{orange}{4}} \\ &{\color{black}=} {\color{red}{4x}} & + {\color{blue} {5y}} &+ \quad ({\color{green}{-6x^2}}) &+{\color{orange}4}}$$
Note that in our result, these terms can appear in any order. It is important to ensure that the signs of each term remain if you move the terms around within the expression. Keeping this in mind, some equivalent forms of the simplified expression above are:
$$-6x^2 +5y+4x+4$$
$$4-6x^2+4x+5y$$
Check your skills by completing the following problems:
1. Combine like terms to simplify: $$3x^2 + 2y^2 + 7y - 2x^2 - 9y + 6y^2$$
Think about it for a moment and then access this link to view answer.
Answer: $$x^2 + 8y^2 - 2y$$
2. Combine like terms to simplify: $$4y^2 + 6y^3 - 7y + 23y^3 - 7y \cdot y - 10$$
Think about it for a moment and then access this link to view answer.
Answer: $$- 3y^2 + 29y^3 - 7y - 10$$
3. Combine like terms to simplify: $$6y^2 - 8z^4 + 9z - 3 + 10x - y$$
Think about it for a moment and then access this link to view answer.
Answer: $$6y^2 - 8z^4 + 9z - 3 + 10x - y$$
(There were no like terms to combine)
4. Combine like terms to simplify: $$6m^2 - 8n^3 + 81m^2 + 42.5m^2 - 12n^3$$
Think about it for a moment and then access this link to view answer.
Answer: $$129.5m^2-20n^3$$
5. Combine like terms to simplify: $$6x^{{1 \over 2}} + 3x^2 - 12x^{{1 \over 2}} + 4x^{ - 2} + 2x^2$$
Think about it for a moment and then access this link to view answer.
Answer: $$- 6x^{{1 \over 2}}+5x^2+4x^{-2} $$