<< Chapter < Page | Chapter >> Page > |
Combine the like terms.
$6\text{\hspace{0.17em}}\text{houses}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4\text{\hspace{0.17em}}\text{houses}=\text{\hspace{0.17em}}10\text{\hspace{0.17em}}\text{houses}$ . 6 and 4 of the same type give 10 of that type.
$6\text{\hspace{0.17em}}\text{houses}+4\text{\hspace{0.17em}}\text{houses}+2\text{\hspace{0.17em}}\text{motels}=10\text{\hspace{0.17em}}\text{houses}+2\text{\hspace{0.17em}}\text{motels}$ . 6 and 4 of the same type give 10 of that type. Thus, we have 10 of one type and 2 of another type.
Suppose we let the letter $x$ represent "house." Then, $6x+4x=10x$ . 6 and 4 of the same type give 10 of that type.
Suppose we let
$x$ represent "house" and
$y$ represent "motel."
Like terms with the same numerical coefficient represent equal amounts of the same quantity.
Like terms with different numerical coefficients represent
different amounts of the same quantity
Since like terms represent amounts of the same quantity, they may be combined, that is, like terms may be added together.
Simplify each of the following polynomials by combining like terms.
$2x+5x+3x$ .
There are
$2x\text{'}\text{s}$ , then 5 more, then 3 more. This makes a total of
$10x\text{'}\text{s}$ .
$2x+5x+3x=10x$
$7x+8y-3x$ .
From
$7x\text{'}\text{s}$ , we lose
$3x\text{'}\text{s}$ . This makes
$4x\text{'}\text{s}$ . The
$8y\text{'}\text{s}$ represent a quantity different from the
$x\text{'}\text{s}$ and therefore will not combine with them.
$7x+8y-3x=4x+8y$
$4{a}^{3}-2{a}^{2}+8{a}^{3}+{a}^{2}-2{a}^{3}$ .
$4{a}^{3},\text{\hspace{0.17em}}8{a}^{3},$ and
$-2{a}^{3}$ represent quantities of the same type.
$4{a}^{3}+8{a}^{3}-2{a}^{3}=10{a}^{3}$
$-2{a}^{2}$ and ${a}^{2}$ represent quantities of the same type.
$-2{a}^{2}+{a}^{2}=-{a}^{2}$
Thus,
$4{a}^{3}-2{a}^{2}+8{a}^{3}+{a}^{2}-2{a}^{3}=10{a}^{3}-{a}^{2}$
Simplify each of the following expressions.
$10{x}^{3}-4{x}^{3}+3{x}^{2}-12{x}^{3}+5{x}^{2}+2x+{x}^{3}+8x$
$-5{x}^{3}+8{x}^{2}+10x$
Simplify each of the following expressions by using the distributive property and combining like terms.
Notification Switch
Would you like to follow the 'Elementary algebra' conversation and receive update notifications?